Results 31 to 40 of about 1,406 (208)
Chromatic symmetric functions in noncommuting variables revisited [PDF]
Advances in Applied Mathematics, 2020 23 pages, final version to appear Adv.
Samantha Dahlberg +1 more
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Positivity of chromatic symmetric functions associated with Hessenberg functions of bounce number 3
, 2022 We give a proof of the Stanley-Stembridge conjecture on chromatic symmetric functions for the class of all unit interval graphs with independence number 3.
Cho, Soojin, Jaehyun Hong
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A deletion–contraction relation for the chromatic symmetric function
European Journal of Combinatorics, 2020 We extend the definition of the chromatic symmetric function $X_G$ to include graphs $G$ with a vertex-weight function $w : V(G) \rightarrow \mathbb{N}$. We show how this provides the chromatic symmetric function with a natural deletion-contraction relation analogous to that of the chromatic polynomial.
Logan Crew, Sophie Spirkl
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On an Algorithm for Comparing the Chromatic Symmetric Functions of Trees [PDF]
Australas. J Comb., 2018 14 ...
Sam Heil, Caleb Ji
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A Two Parameter Chromatic Symmetric Function [PDF]
The Electronic Journal of Combinatorics, 2007 We introduce and develop a two-parameter chromatic symmetric function for a simple graph $G$ over the field of rational functions in $q$ and $t,\,{\Bbb Q}(q,t)$. We derive its expansion in terms of the monomial symmetric functions, $m_{\lambda}$, and present various correlation properties which exist between the two-parameter chromatic symmetric ...
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A Quasisymmetric Function Generalization of the Chromatic Symmetric Function [PDF]
The Electronic Journal of Combinatorics, 2011 The chromatic symmetric function $X_G$ of a graph $G$ was introduced by Stanley. In this paper we introduce a quasisymmetric generalization $X^k_G$ called the $k$-chromatic quasisymmetric function of $G$ and show that it is positive in the fundamental basis for the quasisymmetric functions.
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Extended chromatic symmetric functions and equality of ribbon Schur functions [PDF]
Advances in Applied Mathematics, 2021 Final version to appear Adv.
Farid Aliniaeifard +2 more
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Chromatic classical symmetric functions [PDF]
Journal of Combinatorics, 2018 8 pages, minor adjustments to match final version to appear in J ...
Cho, Soojin, van Willigenburg, Stephanie
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The equivalence of two graph polynomials and a symmetric function
, 2009 The U-polynomial, the polychromate and the symmetric function generalization of the Tutte polynomial due to Stanley are known to be equivalent in the sense that the coefficients of any one of them can be obtained as a function of the coefficients of any ...
Noble, SD +5 more
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Chromatic Symmetric Functions of Hypertrees
The Electronic Journal of Combinatorics, 2017 The chromatic symmetric function $X_H$ of a hypergraph $H$ is the sum of all monomials corresponding to proper colorings of $H$. When $H$ is an ordinary graph, it is known that $X_H$ is positive in the fundamental quasisymmetric functions $F_S$, but this is not the case for general hypergraphs.
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