1,735 research outputs found
Complementary Algorithms For Tableaux
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.Comment: 29 pages, 52 .eps files for figures, JCTA, to appea
Enumeration of Standard Young Tableaux
A survey paper, to appear as a chapter in a forthcoming Handbook on
Enumeration.Comment: 65 pages, small correction
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