An algorithmic sign-reversing involution for special rim-hook tableaux

Egecioglu and Remmel [2] 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 an algorithmic signreversing 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].

• Type: Journal
• Year: 2006
• Where: JAL
• Authors: Bruce E. Sagan, Jaejin Lee
• Keywords: Combinatorial Proof, JAL 2006, Kostka Matrix K-1, Special Rim-hook Tableaux