A sign-reversing involution for rooted special rim-hook tableaux
Combinatorics
2007-05-23 v1
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.
Cite
@article{arxiv.math/0306110,
title = {A sign-reversing involution for rooted special rim-hook tableaux},
author = {Bruce E. Sagan and Jaejin Lee},
journal= {arXiv preprint arXiv:math/0306110},
year = {2007}
}
Comments
13 pages, 6 figures, Latex see related papers at http://www.math.msu.edu/~sagan