3dimensional matrices and Kronecker productsErnesto VallejoInstituto de Matematicas, Morelia, Mexico
April 12,

ABSTRACT


A formula, due to Snapper, gives the number of 3dimensional (0,1)matrices with fixed plane sums as an inner product of certain characters of the symmetric group. Using this formula we give a criterion, in the spirit of the GaleRyser theorem, for deciding when such number is one. We also establish a conexion with the problem of determining the minimal components, in the dominance order, of the Kronecker product of two irreducible characters of the symmetric group. In looking for ways of computing the multiplicity of the minimal components we are led to a onetoone correspondence between 3dimensional (0,1)matrices and certain triples, which uses and generalizes the dual RSKcorrespondence. One application of it is a combinatorial description of those multiplicities in terms of matrices. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

