Jeux de Tableaux

Tom Roby

California State University Hayward

April 12,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

We study four operations defined on pairs of tableaux. Algorithms for the first three involve the familiar procedures of jeu de taquin, row insertion, and column insertion. The fourth operation, hopscotch, is new, although specialised versions have appeared previously. Like the other three operations, this new operation may be computed with a set of local rules in a growth diagram, and it preserves Knuth equivalence class. Each of these four operations gives rise to an a priori distinct theory of dual equivalence. We show that these four theories coincide. The four operations are linked via the involutive tableau operations of complementation and conjugation in an illuminating commutative diagram. We we also show some unusual ways to rectify a skew tableau to normal shape.

This is joint work with Frank Sottile, Jeff Stroomer, and Julian West. A copy of the preprint is available at http://seki.csuhayward.edu.


Speaker's Contact Info: troby(at-sign)csuhayward.edu


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