Row standard tableaux

[AndrewMathas]

Implement row standard tableau in sage, of both partition and partition tuple shape. A row standard tableau is a tableau in which the numbers 1,2,...,n appear in increasing order, from left to right, in each row. These tableau are naturally in bijection with the cosets of the corresponding Young subgroup (or standard parabolic) in the full symmetric group and hence they index bases for various permutation modules, which is why it will be useful to have them.

The shape of a row standard tableau should really be a composition, rather than a partition, but implementing tableau of composition shape would take significantly more effort. For the corresponding modules, up to isomorphism, it is enough to consider row standard tableaux of partition shape so this ticket only considers row standard tableau of partition (tuple) shape. It also defines residue sequences for such tableaux, which are needed in the KLR setting.

The new classes implemented are:

RowStandardTableaux
RowStandardTableaux_all
RowStandardTableaux_size
RowStandardTableaux_shape
RowStandardTableauTuples
RowStandardTableauTuples_all
RowStandardTableauTuples_level
RowStandardTableauTuples_size
RowStandardTableauTuples_level_size
RowStandardTableauTuples_shape
RowStandardTableaux_residue
RowStandardTableaux_residue_shape

Depends on #20564

CC: @sagetrac-sage-combinat @tscrim @darijgr

Component: combinatorics

Keywords: row standard tableaux

Author: Andrew Mathas

Branch/Commit: 4aaa086

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/21162

[AndrewMathas]

Author: Andrew Mathas

[AndrewMathas]

Changed keywords from none to row standard tableaux

[AndrewMathas]

Branch: u/andrew.mathas/row_standard_tableaux

[AndrewMathas]

New commits:

d41fc7d	Implementing row standard tableaux of partition shape
eb8b0ef	Implementing row standard tableaux of partition tuple shape
d88af21	Row standard tableau tuples with residue sequences

[AndrewMathas]

Commit: d88af21

[sagetrac-git]

Changed commit from d88af21 to 0beb237

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

af5a2be	Row standard tableau tuples with residue sequences
bf7646a	Merge branch 'u/andrew.mathas/row_standard_tableaux' of git://trac.sagemath.org/sage into t/21162/row_standard_tableaux
0beb237	Refactoring StandardTableaux as a derived class of RowStandardTableaux

[AndrewMathas]

comment:9

Replying to @sagetrac-git:

Branch pushed to git repo; I updated commit sha1. New commits:

af5a2be	Row standard tableau tuples with residue sequences
bf7646a	Merge branch 'u/andrew.mathas/row_standard_tableaux' of git://trac.sagemath.org/sage into t/21162/row_standard_tableaux
0beb237	Refactoring StandardTableaux as a derived class of RowStandardTableaux

The last commit message is misleading: this commit makes StandardTableauTuples inherit from RowStandardTableauTuples but I ended up leaving StandardTableaux inheriting from SemiStandardTableaux, and not making it inherit from RowStandardTableaux as well, because having it inherit from both wouldn't gain anything and would probably result in a fractional slow-down. The problem is that StandardTableaux now has two natural parents and there is no reason to prefer one over the other so I let the code history in sage decide. Currently this doesn't affect anything because, for example,

sage: [[1,2,3],[4,5]] in RowStandardTableaux()
True
sage: [[1,2,3],[4,5]] in RowStandardTableaux(5)
True
sage: StandardTableau([[1,2,3],[4,5]]) in RowStandardTableaux(5)
True

works as one would expect.

[cheuberg]

comment:10

branch does not merge.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

25e2ecb	Merge branch 'develop' into t/21162/row_standard_tableaux
79778da	Merging into develop and fixing errant doc-tests

[sagetrac-git]

Changed commit from 0beb237 to 79778da

[AndrewMathas]

comment:12

I have merged in to 8.2.rc4. All doc tests pass

---

New commits:

25e2ecb	Merge branch 'develop' into t/21162/row_standard_tableaux
79778da	Merging into develop and fixing errant doc-tests

---

New commits:

25e2ecb	Merge branch 'develop' into t/21162/row_standard_tableaux
79778da	Merging into develop and fixing errant doc-tests

[fchapoton]

comment:13

patchbot is not happy at all, see the failing plugins

[sagetrac-git]

Changed commit from 85d2e3e to 4de8a8b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. Last 10 new commits:

e908d59	Adding q-analogs used in quantum groups.
f4bba3e	Merge branch 'public/quantum_groups/q_numbers-25067' into public/modules/fock_space
b4f73fa	Minor tweaks to documentation
d139e28	Merge branch 'public/modules/fock_space' of git://trac.sagemath.org/sage into public/combinat/kleshchev_partitoins-20564
e78de6c	Fixing duplicate references.
cadff7b	Adding mathscinet links
88b72f1	Merge branch '8.3.beta0 develop' into t/20564/public/combinat/kleshchev_partitoins-20564
f3fc941	Making KleshchevPartitions a lazy import
8263e74	A few other touchups.
4de8a8b	Merge branch 'public/combinat/row_standard_tableaux-21162' of git://trac.sagemath.org/sage into public/combinat/row_standard_tableaux-21162

[tscrim]

Dependencies: #20564

[tscrim]

comment:43

I just decided to beat it to the punch so both tickets could be merged in the same beta. Trivial rebase.

[darijgr]

comment:44

+.. [DJM1999] \R. Dipper, G. James and A. Mathas
+             *The cyclotomic q-Schur algebra*, Math. Z, **229** (1999), 385-416.
+             :mathscinet:`MR1635149`

Isn't it "Cyclotomic q-Schur algebras" or am I getting two papers confused?

[sagetrac-git]

Changed commit from 4de8a8b to 2bc9534

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

2bc9534

Fixing DJM reference

[sagetrac-git]

Changed commit from 2bc9534 to 4d19ecd

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

4d19ecd

Fixing mathscinet reference

[AndrewMathas]

comment:47

That's embarrassing! I had the title wrong. The year wrong and the mathscinet reference wrong:(

[kiwifb]

comment:48

Documentation fails to build

.. [BKW2011]_ \J. Brundan, A. Kleshchev, and W. Wang,

shouldn't have _ like other entries.

[sagetrac-git]

Changed commit from 4d19ecd to 4aaa086

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

ba22b7f	Merge branch 'develop' into t/20564/public/combinat/kleshchev_partitoins-20564
5e5719e	Merge branch 'public/combinat/row_standard_tableaux-21162' of git://trac.sagemath.org/sage into public/combinat/row_standard_tableaux-21162
4aaa086	Fixing the docbuild.

[tscrim]

comment:50

Fixed. Thank you for catching that.

Also rebased over the latest develop and #20564.

[AndrewMathas]

comment:51

Thanks Travis!

[vbraun]

Changed branch from public/combinat/row_standard_tableaux-21162 to 4aaa086