#20587: Residues and degrees for tableaux
-------------------------------------+-------------------------------------
Reporter: andrew.mathas | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-7.3
Component: combinatorics | Resolution:
Keywords: tableaux, rsidue | Merged in:
sequences, tableaux degrees | Reviewers:
Authors: Andrew Mathas | Work issues:
Report Upstream: N/A | Commit:
Branch: | ee10fcc319b21d65e380acd686a21c57a816d488
u/andrew.mathas/residues_and_degrees_for_tableaux| Stopgaps:
Dependencies: #20564 |
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Changes (by tscrim):
* dependencies: => #20564
Old description:
> Residue sequences of tableaux are an important statistic, particularly in
> the non-semisimple and graded representation theories. This ticket
> implements two classes `ResidueSequence` and its parent class
> `ResidueSequences` for these sequences, In addition, it implement the
> Brundan-Kleshchev-Wang degree function on tableaux and tableaux tuples.
> In practice, these are all implemented as methods on tableaux and
> tableaux tuples:
> {{{#!python
> sage:
> StandardTableau([[1,2,3],[4,5]]).residue_sequence(3).standard_tableaux()
> Standard tableaux of residue (0,1,2,2,0)
> Tableau([[1,2,5],[3,4]]).degree(3)
> 0
> sage:
> StandardTableauTuple([[[5]],[[1,2],[3,4]]]).residue_sequence(3,[0,0])
> 3-residue sequence (0,1,2,0,0) with multicharge (0,0)
> sage: StandardTableauTuple([[[2,8],[7]],[[1,4,6],[3,5]]]).degree(0,(0,1))
> 1
> }}}
> As an added bonus, we convert `TableauTuples` to ClonableArrays`.
New description:
Residue sequences of tableaux are an important statistic, particularly in
the non-semisimple and graded representation theories. This ticket
implements two classes `ResidueSequence` and its parent class
`ResidueSequences` for these sequences, In addition, it implement the
Brundan-Kleshchev-Wang degree function on tableaux and tableaux tuples. In
practice, these are all implemented as methods on tableaux and tableaux
tuples:
{{{#!python
sage:
StandardTableau([[1,2,3],[4,5]]).residue_sequence(3).standard_tableaux()
Standard tableaux of residue (0,1,2,2,0)
Tableau([[1,2,5],[3,4]]).degree(3)
0
sage:
StandardTableauTuple([[[5]],[[1,2],[3,4]]]).residue_sequence(3,[0,0])
3-residue sequence (0,1,2,0,0) with multicharge (0,0)
sage: StandardTableauTuple([[[2,8],[7]],[[1,4,6],[3,5]]]).degree(0,(0,1))
1
}}}
As an added bonus, we convert `TableauTuples` to use `ClonableArray`.
--
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Ticket URL: <http://trac.sagemath.org/ticket/20587#comment:6>
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