A COMBINATORIAL INTERPRETATION FOR THE COEFFICIENTS IN THE KRONECKER PRODUCT s(n p;p) s

Abstract

In this paper we give a combinatorial interpretation for the coecien t of s in the Kronecker product s(n p;p) s , where = ( 1; : : : ; '( )) ' n, if '( ) 2p 1 or 1 2p 1; that is, if is not a partition inside the 2(p 1) 2(p 1) square. For inside the square our combinatorial interpretation provides an upper bound for the coecien ts. In general, we are able to combinatorially compute these coecien ts for all 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.