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src/doc/en/reference/combinat/index.rst

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module_list
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See also
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.. toctree::
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:maxdepth: 1
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sage/rings/cfinite_sequence
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.. include:: ../footer.txt
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src/doc/en/reference/combinat/module_list.rst

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Comprehensive Module List
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=========================
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.. This list is currently sorted in alphabetical order with respect to the module names.
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It can be updated semi-automatically by running in ``src/sage/combinat``::
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.. NOTE::
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find . -type f \( -name "*.py" -o -name "*.pyx" \) | sed 's/\.pyx\?$//; s|^\./| sage/combinat/|' | LC_ALL=C sort > /tmp/module_list.rst
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This list is currently sorted in alphabetical order with respect to the module names.
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It can be updated semi-automatically by running in ``src/sage/combinat``::
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and copy pasting the result back there.
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find . -type f \( -name "*.py" -o -name "*.pyx" \) | sed 's/\.pyx\?$//; s|^\./| sage/combinat/|' | LC_ALL=C sort > /tmp/module_list.rst
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See Issue #17421 for desirable improvements.
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and copy pasting the result back there.
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See :issue:`17421` for desirable improvements.
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.. toctree::
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:maxdepth: 1
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sage/combinat/growth
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sage/combinat/hall_polynomial
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sage/combinat/hillman_grassl
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sage/combinat/integer_lists/__init__
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sage/combinat/integer_lists/base
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sage/combinat/integer_lists/invlex
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sage/combinat/integer_lists/lists

src/sage/combinat/SJT.py

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r"""
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The Steinhaus-Johnson-Trotter algorithm
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The Steinhaus-Johnson-Trotter algorithm generates all permutations of a list in
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an order such that each permutation is obtained by transposing two adjacent
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elements from the previous permutation.

src/sage/combinat/blob_algebra.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Blob Algebras
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Blob algebras
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AUTHORS:
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src/sage/combinat/cartesian_product.py

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r"""
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Cartesian Products
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Cartesian products
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"""
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# ****************************************************************************
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# Copyright (C) 2007 Mike Hansen <[email protected]>,

src/sage/combinat/cluster_algebra_quiver/cluster_seed.py

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# sage.doctest: needs sage.graphs sage.modules
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r"""
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ClusterSeed
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Cluster seeds
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A *cluster seed* is a pair `(B,\mathbf{x})` with `B` being a *skew-symmetrizable* `(n+m) \times n` *-matrix*
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and with `\mathbf{x}` being an `n`-tuple of *independent elements* in the field of rational functions in `n` variables.
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A *cluster seed* is a pair `(B,\mathbf{x})` with `B` being a
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*skew-symmetrizable* `(n+m) \times n` *-matrix* and with `\mathbf{x}` being an
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`n`-tuple of *independent elements* in the field of rational functions in `n`
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variables.
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For the compendium on the cluster algebra and quiver package see
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[MS2011]_.
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AUTHORS:
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- Gregg Musiker: Initial Version
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- Christian Stump: Initial Version
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- Aram Dermenjian (2015-07-01): Updating ability to not rely solely on clusters
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- Jesse Levitt (2015-07-01): Updating ability to not rely solely on clusters
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REFERENCES:
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2015
- [FZ2007]_
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- [BDP2013]_
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.. SEEALSO:: For mutation types of cluster seeds, see :meth:`sage.combinat.cluster_algebra_quiver.quiver_mutation_type.QuiverMutationType`. Cluster seeds are closely related to :meth:`sage.combinat.cluster_algebra_quiver.quiver.ClusterQuiver`.
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.. SEEALSO::
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For mutation types of cluster seeds, see
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:meth:`sage.combinat.cluster_algebra_quiver.quiver_mutation_type.QuiverMutationType`.
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Cluster seeds are closely related to
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:meth:`sage.combinat.cluster_algebra_quiver.quiver.ClusterQuiver`.
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AUTHORS:
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- Gregg Musiker: initial version
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- Christian Stump: initial version
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- Aram Dermenjian (2015-07-01): updating ability to not rely solely on clusters
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- Jesse Levitt (2015-07-01): updating ability to not rely solely on clusters
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"""
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# ****************************************************************************

src/sage/combinat/cluster_algebra_quiver/interact.py

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r"""
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Interactive window for cluster seed mutations
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"""
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import ipywidgets as widgets
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from sage.misc.latex import latex
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from sage.repl.rich_output.pretty_print import pretty_print

src/sage/combinat/colored_permutations.py

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r"""
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Colored Permutations
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Colored permutations
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.. TODO::
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src/sage/combinat/composition_signed.py

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r"""
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Signed Compositions
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Signed compositions
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"""
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# ****************************************************************************
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# Copyright (C) 2007 Mike Hansen <[email protected]>,

src/sage/combinat/composition_tableau.py

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r"""
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Composition Tableaux
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Composition tableaux
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AUTHORS:
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- Chris Berg, Jeff Ferreira (2012-9): Initial version
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- Chris Berg, Jeff Ferreira (2012-9): initial version
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"""
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from sage.sets.disjoint_union_enumerated_sets import DisjointUnionEnumeratedSets
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from sage.sets.non_negative_integers import NonNegativeIntegers

src/sage/combinat/crystals/affine.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Affine Crystals
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Affine crystals
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"""
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# ****************************************************************************
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# Copyright (C) 2008 Brant Jones <brant at math.ucdavis.edu>

src/sage/combinat/crystals/affinization.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Affinization Crystals
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Affinization crystals
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"""
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#*****************************************************************************

src/sage/combinat/crystals/catalog.py

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r"""
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Catalog Of Crystals
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Catalog of crystals
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Let `I` be an index set and let `(A,\Pi,\Pi^\vee,P,P^\vee)` be a Cartan datum
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associated with generalized Cartan matrix `A = (a_{ij})_{i,j\in I}`. An

src/sage/combinat/crystals/catalog_elementary_crystals.py

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"""
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Catalog Of Elementary Crystals
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Catalog of elementary crystals
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See :mod:`~sage.combinat.crystals.elementary_crystals`.
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src/sage/combinat/crystals/catalog_infinity_crystals.py

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r"""
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Catalog Of Crystal Models For `B(\infty)`
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Catalog of crystal models For `B(\infty)`
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We currently have the following models:
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src/sage/combinat/crystals/catalog_kirillov_reshetikhin.py

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"""
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Catalog Of Crystal Models For Kirillov-Reshetikhin Crystals
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Catalog of crystal models for Kirillov-Reshetikhin crystals
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We currently have the following models:
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src/sage/combinat/crystals/direct_sum.py

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# sage.doctest: needs sage.combinat sage.modules
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"""
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Direct Sum of Crystals
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Direct sum of crystals
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"""
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#*****************************************************************************
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# ****************************************************************************
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# Copyright (C) 2010 Anne Schilling <anne at math.ucdavis.edu>
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#
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# Distributed under the terms of the GNU General Public License (GPL)
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# The full text of the GPL is available at:
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#
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# http://www.gnu.org/licenses/
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#****************************************************************************
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# ***************************************************************************
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from sage.categories.category import Category
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from sage.sets.disjoint_union_enumerated_sets import DisjointUnionEnumeratedSets

src/sage/combinat/crystals/elementary_crystals.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Elementary Crystals
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Elementary crystals
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Let `\lambda` be a weight. The crystals `T_{\lambda}`, `R_{\lambda}`, `B_i`,
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and `C` are important objects in the tensor category of crystals.

src/sage/combinat/crystals/fast_crystals.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Fast Rank Two Crystals
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Fast rank two crystals
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"""
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# ****************************************************************************
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# Copyright (C) 2007 Anne Schilling <anne at math.ucdavis.edu>

src/sage/combinat/crystals/generalized_young_walls.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Crystals of Generalized Young Walls
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AUTHORS:
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- Lucas David-Roesler: Initial version
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- Ben Salisbury: Initial version
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- Travis Scrimshaw: Initial version
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Crystals of generalized Young walls
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Generalized Young walls are certain generalizations of Young tableaux
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introduced in [KS2010]_ and designed to be a realization of the crystals
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- [KLRS2016]_
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- [KS2010]_
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AUTHORS:
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- Lucas David-Roesler: initial version
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- Ben Salisbury: initial version
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- Travis Scrimshaw: initial version
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"""
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# *****************************************************************************

src/sage/combinat/crystals/induced_structure.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Induced Crystals
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Induced crystals
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We construct a crystal structure on a set induced by a bijection `\Phi`.
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- Travis Scrimshaw (2014-05-15): Initial implementation
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- Travis Scrimshaw (2014-05-15): initial implementation
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"""
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#*****************************************************************************

src/sage/combinat/crystals/infinity_crystals.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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`\mathcal{B}(\infty)` Crystals of Tableaux in Nonexceptional Types and `G_2`
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`\mathcal{B}(\infty)` crystals of tableaux in nonexceptional types and `G_2`
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A tableau model for `\mathcal{B}(\infty)`. For more information, see
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:class:`~sage.combinat.crystals.infinity_crystals.InfinityCrystalOfTableaux`.
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AUTHORS:
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- Ben Salisbury: Initial version
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- Travis Scrimshaw: Initial version
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- Ben Salisbury: initial version
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- Travis Scrimshaw: initial version
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"""
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#*****************************************************************************

src/sage/combinat/crystals/kirillov_reshetikhin.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Kirillov-Reshetikhin Crystals
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Kirillov-Reshetikhin crystals
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"""
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# ****************************************************************************

src/sage/combinat/crystals/kyoto_path_model.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Kyoto Path Model for Affine Highest Weight Crystals
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Kyoto path model for affine highest weight crystals
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#*****************************************************************************
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# ***************************************************************************
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# Copyright (C) 2013 Travis Scrimshaw <tscrim at ucdavis.edu>
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#
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# Distributed under the terms of the GNU General Public License (GPL)
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# The full text of the GPL is available at:
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#
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#****************************************************************************
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# ***************************************************************************
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from sage.structure.parent import Parent
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from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets

src/sage/combinat/crystals/monomial_crystals.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Crystals of Modified Nakajima Monomials
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AUTHORS:
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- Arthur Lubovsky: Initial version
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- Ben Salisbury: Initial version
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Crystals of modified Nakajima monomials
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Let `Y_{i,k}`, for `i \in I` and `k \in \ZZ`, be a commuting set of
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variables, and let `\boldsymbol{1}` be a new variable which commutes with
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`C = (c_{ij})_{i\neq j}` satisfying the condition `c_{ij}+c_{ji}=1`.
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We have chosen such integers uniformly such that `c_{ij} = 1` if
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`i < j` and `c_{ij} = 0` if `i>j`.
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AUTHORS:
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- Arthur Lubovsky: initial version
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- Ben Salisbury: initial version
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"""
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# *****************************************************************************

src/sage/combinat/crystals/multisegments.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Crystal of Bernstein-Zelevinsky Multisegments
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Crystal of Bernstein-Zelevinsky multisegments
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"""
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#*****************************************************************************

src/sage/combinat/crystals/mv_polytopes.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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Crystal Of Mirković-Vilonen (MV) Polytopes
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Crystal of Mirković-Vilonen polytopes
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AUTHORS:
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src/sage/combinat/crystals/pbw_crystal.py

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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`\mathcal{B}(\infty)` Crystal Of PBW Monomials
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AUTHORS:
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- Dinakar Muthiah (2015-05-11): initial version
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`\mathcal{B}(\infty)` crystal of PBW monomials
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.. SEEALSO::
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For information on PBW datum, see
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:ref:`sage.combinat.crystals.pbw_datum`.
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AUTHORS:
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- Dinakar Muthiah (2015-05-11): initial version
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"""
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# ****************************************************************************

src/sage/combinat/crystals/pbw_datum.pyx

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# sage.doctest: needs sage.combinat sage.modules
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r"""
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PBW Data
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PBW data
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This contains helper classes and functions which encode PBW data
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in finite type.

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