Symmetric and quasi-symmetric functions associated to polymatroids

被引：0
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作者：
Derksen, Harm [1 ]
机构：
[1] Department of Mathematics, University of Michigan, East Hall, 530 Church Street, Ann Arbor, MI 48109-1043, United States
来源：
Journal of Algebraic Combinatorics | 2009年 / 30卷 / 01期
关键词：
To every subspace arrangement X we will associate symmetric functions ℘[X] and ℋ [X]. These symmetric functions encode the Hilbert series and the minimal projective resolution of the product ideal associated to the subspace arrangement. They can be defined for discrete polymatroids as well. The invariant ℋ [X] specializes to the Tutte polynomial {T X] . Billera; Jia and Reiner recently introduced a quasi-symmetric function F [X] (for matroids) which behaves valuatively with respect to matroid base polytope decompositions. We will define a quasi-symmetric function {G}{X} for polymatroids which has this property as well. Moreover; {G}}{X} specializes to ℘ [X; ℋ; X; {T}{X} and F [X]. © 2008 Springer Science+Business Media; LLC;
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页码：43 / 86
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