On the diagonal ideal of (C) and q, t-Catalan numbers
نویسندگان
چکیده
Let In be the (big) diagonal ideal of (C). Haiman proved that the q, t-Catalan number is the Hilbert series of the graded vector space Mn = ⊕ d1,d2 (Mn)d1,d2 spanned by a minimal set of generators for In. We give simple upper bounds on dim (Mn)d1,d2 in terms of partition numbers, and find all bi-degrees (d1, d2) such that dim (Mn)d1,d2 achieve the upper bounds. For such bi-degrees, we also find explicit bases for (Mn)d1,d2 . Résumé. Soit In l’idéal de la (grande) diagonale de (C). Haiman a démontré que le q, t-nombre de Catalan est la série de Hilbert de l’espace vectoriel gradué Mn = ⊕ d1,d2 (Mn)d1,d2 engendré par un ensemble minimal de générateurs de In. Nous obtenons des bornes supérieures simples pour dim (Mn)d1,d2 en termes de nombres de partitions, ainsi que tous les bi-degrés (d1, d2) pour lesquels ces bornes supérieures sont atteintes. Pour ces bi–degrés, nous trouvons aussi des bases explicites de (Mn)d1,d2 .
منابع مشابه
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