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

Bruce E. Sagan·Jaejin Lee
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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^{-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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Bruce E. Sagan, Jaejin Lee. 2003-06-06. A sign-reversing involution for rooted special rim-hook tableaux. https://arxiv.org/abs/math/0306110

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