Séminaire Lotharingien de Combinatoire, B54Af (2006), 29 pp.

Cristina M. Ballantine and Rosa C. Orellana

A Combinatorial Interpretation for the Coefficients in the Kronecker Product s(n-p,p)*s\lambda

Abstract. In this paper we give a combinatorial interpretation for the coefficient of s\nu in the Kronecker product s(n-p,p)*s\lambda, where \lambda=(\lambda1, ..., \lambdal(\lambda)) is a partition of n, if l(\lambda)>=2p-1 or \lambda1>=2p-1; that is, if \lambda is not a partition inside the 2(p-1) x 2(p-1) square. For \lambda inside the square our combinatorial interpretation provides an upper bound for the coefficients. In general, we are able to combinatorially compute these coefficients for all \lambda when n>(2p-2)2. We use this combinatorial interpretation to give characterizations for multiplicity free Kronecker products. We have also obtained some formulas for special cases.

Received: October 10, 2005. Accepted: September 1, 2006. Final Version: September 6, 2006.

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Corrigendum

On page 25, line -6, in Corollary 4.13, $ \displaystyle m_4=\min\left\{ s,p-s, \left\lfloor\frac{p+s-t}{2}\right\rfloor\right\}$ should be replaced by $ \displaystyle m_4=\min\left\{ s,p-s-1, \left\lfloor\frac{p+s-t}{2}\right\rfloor\right\}$.