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

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

2003-06-06

arxiv.org/abs/math/0306110v1

Mathematics

Combinatorics

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

Scientific paper

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^{-1}K=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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