A Sign-reversing Involution for Rooted Special Rim-hook Tableaux

Abstract

Eg̃eciog̃lu and Remmel [2] gave an interpretation for the entries of the inverse Kostka matrix K in terms of special rim-hook tableaux. They were able to use this interpretation to give a combinatorial proof that KK = I but were unable to do the same for the equation KK = 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 [1] we combine our involution with a result of Gasharov [5] to give a combinatorial proof of a special case of the (3+1)-free Conjecture of Stanley and Stembridge [14].

Cite this paper

@inproceedings{Sagan2003ASI, title={A Sign-reversing Involution for Rooted Special Rim-hook Tableaux}, author={Bruce E. Sagan}, year={2003} }