Diagonal invariants and the refined multimahonian distribution

Details Diagonal invariants and the refined multimahonian distribution Diagonal invariants and the refined multimahonian distribution

2008-05-19

arxiv.org/abs/0805.2860v2

Mathematics

Combinatorics

18 pages

Scientific paper

Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are a pure combinatorial algorithm to describe the irreducible decomposition of the tensor product of two irreducible representations of the symmetric group, and new symmetry results on permutation enumeration with respect to descent sets.

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