#17780: Robinson-Schensted Generalization to Type B
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Reporter: cahlbach | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.5
Component: combinatorics | Resolution:
Keywords: Type B, signed permutations, | Merged in:
Robinson-Schensted | Reviewers:
Authors: Connor Ahlbach | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Old description:
> Debra Garfinkle defined an algorithm which sends a signed permutation to
> a pair of standard domino tableaux, which each entry 1,2,.. n appears as
> a domino instead of a single cell, and rows and columns remain
> increasing. The algorithm is similar to the Robinson-Schensted
> correspondence on permutations. We implement it here. We also include an
> algorithm which moves a domino tableaux through open cycles, and one
> which specializes it to one of special shape. This algorithm has
> applications to representation theory and Kazhdan-Lustig cells. Note that
> signed permutations are lists of the form [[a_1,e_1], ... [a_n,e_n]]
> where [a_1, ... a_n] is a permutation, and e_n are just 1 or -1. Domino
> tableaux are listed just like tableaux.
New description:
Debra Garfinkle defined an algorithm which sends a signed permutation to a
pair of standard domino tableaux, which each entry `1, 2, ..., n` appears
as a domino instead of a single cell, and rows and columns remain
increasing. The algorithm is similar to the Robinson-Schensted
correspondence on permutations. We implement it here. We also include an
algorithm which moves a domino tableaux through open cycles, and one which
specializes it to one of special shape. This algorithm has applications to
representation theory and Kazhdan-Lustig cells. Note that signed
permutations are lists of the form `[[a_1,e_1], ... [a_n,e_n]]` where
`[a_1, ... a_n]` is a permutation, and `e_n` are just `1` or `-1`. Domino
tableaux are listed just like tableaux.
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Comment (by tscrim):
You might also be interested in #16010 and #17411.
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Ticket URL: <http://trac.sagemath.org/ticket/17780#comment:1>
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