Symmetric and quasi-symmetric functions associated to polymatroids

被引：0
|
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;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Journal article (JA)
引用
收藏
页码：43 / 86
相关论文
共 50 条
  • [31] The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions
    Nantel Bergeron
    Juana Sánchez-Ortega
    Mike Zabrocki
    Annals of Combinatorics, 2016, 20 : 283 - 300
  • [32] Hecke algebras, difference operators, and quasi-symmetric functions
    Hivert, F
    ADVANCES IN MATHEMATICS, 2000, 155 (02) : 181 - 238
  • [33] Shifted quasi-symmetric functions and the Hopf algebra of peak functions
    Bergeron, N
    Mykytiuk, S
    Sottile, F
    van Willigenburg, S
    DISCRETE MATHEMATICS, 2002, 246 (1-3) : 57 - 66
  • [34] Algebra of operators on the ring of polytopes and quasi-symmetric functions
    Buchstaber, V. M.
    Erokhovets, N. Yu.
    RUSSIAN MATHEMATICAL SURVEYS, 2010, 65 (02) : 381 - 383
  • [35] Bidendriform bialgebras, trees, and free quasi-symmetric functions
    Foissy, Loic
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2007, 209 (02) : 439 - 459
  • [36] Quasi-symmetric functions and up-down compositions
    Fuller, Evan
    Remmel, Jeffrey
    DISCRETE MATHEMATICS, 2011, 311 (16) : 1754 - 1767
  • [37] Inversion of some series of free quasi-symmetric functions
    Hivert, Florent
    Novelli, Jean-Christophe
    Thibon, Jean-Yves
    EUROPEAN JOURNAL OF COMBINATORICS, 2010, 31 (01) : 29 - 33
  • [38] The algebra of quasi-symmetric functions is free over the integers
    Hazewinkel, M
    ADVANCES IN MATHEMATICS, 2001, 164 (02) : 283 - 300
  • [39] The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions
    Bergeron, Nantel
    Sanchez-Ortega, Juana
    Zabrocki, Mike
    ANNALS OF COMBINATORICS, 2016, 20 (02) : 283 - 300
  • [40] CLASSIFICATION OF QUASI-SYMMETRIC DOMAINS
    SATAKE, I
    NAGOYA MATHEMATICAL JOURNAL, 1976, 62 (SEP) : 1 - 12
12345