Degrees of Stretched Kostka Coefficients
نویسنده
چکیده
Given a partition λ and a composition β, the stretched Kostka coefficient Kλβ(n) is the map n 7→ Knλ,nβ sending each positive integer n to the Kostka coefficient indexed by nλ and nβ. Derksen and Weyman [DW02] have shown that stretched Kostka coefficients are polynomial functions of n. King, Tollu, and Toumazet have conjectured that these polynomials always have nonnegative coefficients [KTT04], and they have given a conjectural expression for their degrees [KTT]. We prove the values conjectured by King, Tollu, and Toumazet for the degrees of stretched Kostka coefficients. Our proof depends on the polyhedral geometry of Gelfand–Tsetlin polytopes and uses tilings of GT-patterns, a combinatorial structure introduced in [DLM04].
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