A sign-reversing involution for rooted special rim-hook tableaux

2003/06/06 by Bruce E. Sagan, Sagan, Bruce E., Jaejin Lee +1
Mathematics · #05E05 #05E10 (Primary) 05A17 #06A11 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A17 #msc:05E05 #msc:05E10 #msc:06A11

paper · pdf · doi:10.48550/arxiv.math/0306110

13 pages, 6 figures, Latex see related papers at http://www.math.msu.edu/~sagan

arxiv created 2003/06/06 · arxiv updated 2009/11/30

Abstract

Egecioglu and Remmel gave an interpretation for the entries of the inverse Kostka matrix K^-1 in terms of special rim-hook tableaux. They were able to use this interpretation to give a combinatorial proof that KK^-1=I but were unable to do the same for the equation K^-1K=I. We define a sign-reversing involution on rooted special rim-hook tableaux which can be used to prove that the last column of this second product is correct. In addition, following a suggestion of Chow we combine our involution with a result of Gasharov to give a combinatorial proof of a special case of the (3+1)-free Conjecture of Stanley and Stembridge.

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