The Hive Model and the Factorisation of Kostka Coefficients
نویسندگان
چکیده
The hive model is used to explore the properties of both Kostka coefficients and stretched Kostka coefficient polynomials. It is shown that both of these may factorise, and that they can then be expressed as products of certain primitive coefficients and polynomials, respectively. It is further shown how to determine a sequence of linear factors (t+m) of the primitive polynomials, where t is the stretching parameter, as well as a bound on their degree in the form of a simple formula which is conjectured to be exact. Résumé. Nous utilisons le modèle des ruches pour étudier les propriétés des cœfficients de Kostka et des polynômes associés aux cœfficients de Kostka dilatés. Nous montrons que les uns et les autres peuvent se factoriser : ils s’écrivent comme des produits de cœfficients (respectivement polynômes) primitifs. En outre, nous montrons comment établir une suite de facteurs linéaires (t+m) des polynômes primitifs (t est le paramètre de dilatation), et proposons une formule simple donnant une borne supérieure de leur degré.
منابع مشابه
Degrees of Stretched Kostka Coefficients
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]...
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