A `nice' bijection for a content formula for skew semistandard Young tableaux

2000/11/30 by Martin Rubey
Mathematics · #math.CO #msc:05E10

paper · pdf

published as Electronic Journal of Combinatorics 9 (2002), #R18 · 13 pages, LaTeX

arxiv created 2002/05/20 · arxiv updated 2009/11/30

Abstract

Based on Schützenberger's evacuation and a modification of jeu de taquin, we give a bijective proof of an identity connecting the generating function of reverse semistandard Young tableaux with bounded entries with the generating function of all semistandard Young tableaux. This solves Exercise 7.102 b of Richard Stanley's book `Enumerative Combinatorics 2'.

Related

• Bijections for an identity of Young Tableaux
• Generating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers
• Inversions of Semistandard Young Tableaux
• Minimal skew semistandard tableaux and the Hillman--Grassl correspondence
• Another involution principle-free bijective proof of Stanley's hook-content formula