#17780: Robinson-Schensted Generalization to Type B
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Reporter: cahlbach | Owner:
Type: | Status: new
enhancement | Milestone: sage-6.5
Priority: major | Keywords: Type B, signed permutations,
Component: | Robinson-Schensted
combinatorics | Authors: Connor Ahlbach
Merged in: | Report Upstream: N/A
Reviewers: | Branch:
Work issues: | Dependencies:
Commit: |
Stopgaps: |
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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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Ticket URL: <http://trac.sagemath.org/ticket/17780>
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