Complementary Algorithms For Tableaux

Details Complementary Algorithms For Tableaux Complementary Algorithms For Tableaux

2000-02-28

arxiv.org/abs/math/0002244v2

J. Combin. Th. Ser. A, 96, No. 1, October 2001, 127-161.

Mathematics

Combinatorics

29 pages, 52 .eps files for figures, JCTA, to appear

Scientific paper

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.

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