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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*=(*\lambda*_{1},
..., *\lambda*_{l(\lambda)}) is a
partition
of *n*, if *l*(*\lambda*)>=2*p*-1 or
*\lambda*_{1}>=2*p*-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*>(2*p*-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.

The following versions are available:

## Corrigendum

On page 25, line -6, in Corollary 4.13,
should be
replaced by
.