3-dimensional matrices and Kronecker products

Ernesto Vallejo

Instituto de Matematicas, Morelia, Mexico

April 12,
refreshments at 3:45pm


A formula, due to Snapper, gives the number of 3-dimensional (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 Gale-Ryser 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 one-to-one correspondence between 3-dimensional (0,1)-matrices and certain triples, which uses and generalizes the dual RSK-correspondence. One application of it is a combinatorial description of those multiplicities in terms of matrices.

Speaker's Contact Info: vallejo(at-sign)matmor.unam.mx

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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