3,281 research outputs found

    Polynomiality of certain average weights for oscillating tableaux

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    We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived.Comment: 12 page

    Difference operators for partitions under the Littlewood decomposition

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    The concept of tt-difference operator for functions of partitions is introduced to prove a generalization of Stanley's theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of tt-hooks. It is well-known that the hook lengths of multiples of tt can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo tt.Comment: 24 page
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