Chromatic bases for symmetric functions

被引：0
|
作者：
Cho, Soojin [1 ]
van Willigenburg, Stephanie [2 ]
机构：
[1] Ajou Univ, Dept Math, Suwon 443749, South Korea
[2] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2016年 / 23卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
chromatic symmetric function; complete graph; star graph; path; cycle;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if {G(k)}(k >= 1) is a set of connected graphs such that G(k) has k vertices for each k, then the set of all chromatic symmetric functions {XG(k)}(k >= 1) generates the algebra of symmetric functions. We also obtain explicit expressions for the generators arising from complete graphs, star graphs, path graphs and cycle graphs.
引用
收藏
页数：7
相关论文
共 50 条
  • [41] Binary shuffle bases for quasi-symmetric functions
    Jean-Christophe Novelli
    Jean-Yves Thibon
    The Ramanujan Journal, 2016, 40 : 207 - 225
  • [42] On Quasibases and Bases of Symmetric Spaces Consisting of Nonnegative Functions
    Astashkin, S. V.
    Terekhin, P. A.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2022, 319 (01) : 13 - 21
  • [43] Binary shuffle bases for quasi-symmetric functions
    Novelli, Jean-Christophe
    Thibon, Jean-Yves
    RAMANUJAN JOURNAL, 2016, 40 (01): : 207 - 225
  • [44] Descents, Quasi-Symmetric Functions, Robinson-Schensted for Posets, and the Chromatic Symmetric Function
    Timothy Y. Chow
    Journal of Algebraic Combinatorics, 1999, 10 : 227 - 240
  • [45] Descents, quasi-symmetric functions, Robinson-Schensted for posets, and the chromatic symmetric function
    Chow, TY
    JOURNAL OF ALGEBRAIC COMBINATORICS, 1999, 10 (03) : 227 - 240
  • [46] Chromatic symmetric functions of Dyck paths and q-rook theory
    Colmenarejo, Laura
    Morales, Alejandro H.
    Panova, Greta
    EUROPEAN JOURNAL OF COMBINATORICS, 2023, 107
  • [47] Dual bases for noncommutative symmetric and quasi-symmetric functions via monoidal factorization
    Bui, V. C.
    Duchamp, G. H. E.
    Minh, V. Hoang Ngoc
    Kane, L.
    Tollu, C.
    JOURNAL OF SYMBOLIC COMPUTATION, 2016, 75 : 56 - 73
  • [48] ON BIDUAL BASES IN THE SPACE OF SYMMETRIC ANALYTIC FUNCTIONS ON l(1)
    Holubchak, O. M.
    Zagorodnyuk, A., V
    CARPATHIAN MATHEMATICAL PUBLICATIONS, 2013, 5 (01) : 47 - 49
  • [49] Subspace filters and polar bases for spaces of symmetric multilinear functions
    Pate, Thomas H.
    LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (10): : 2076 - 2100
  • [50] On symmetric functions and symmetric functions of symmetric functions
    O'Toole, AL
    ANNALS OF MATHEMATICAL STATISTICS, 1931, 2 : 103 - 149
12345