Results 41 to 50 of about 2,074 (148)
A deletion-contraction long exact sequence for chromatic symmetric homology
, 2023 Crew and Spirklt generalize Stanley's chromatic symmetric function to vertex-weighted graphs. One of the primary motivations for extending the chromatic symmetric function to vertex-weighted graphs is the existence of a deletion-contraction relation in ...
Ciliberti, Azzurra
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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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Counting Subtrees Using the Chromatic Symmetric Function
, 2023 In 1995 Richard Stanley defined the chromatic symmetric function as a generalization of the chromatic polynomial. In the same paper Stanley gave a expansion of the chromatic symmetric function in the power-sum basis for symmetric functions.
Salcido, Enrique
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On chromatic symmetric homology and planarity of graphs
, 2022 Sazdanovic and Yip defined a categorification of Stanley's chromatic function called the chromatic symmetric homology. In this paper we prove that (as conjectured by Chandler, Sazdanovic, Stella and Yip), if a graph $G$ is non-planar, then its chromatic ...
Luca Moci +5 more
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Reinforcement learning the chromatic symmetric function
Advances in Theoretical and Mathematical PhysicsWe propose a conjectural counting formula for the coefficients of the chromatic symmetric function of unit interval graphs using reinforcement learning. The formula counts specific disjoint cycle-tuples in the graphs, referred to as Eschers, which satisfy certain concatenation conditions.
Gergely Bérczi, Jonas Klüver
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Proper caterpillars are distinguished by their symmetric chromatic function [PDF]
, 2012 . This paper deals with the so-called Stanley conjecture, which asks whether they are non-isomorphic trees with the same symmetric function generalization of the chromatic polynomial.
Aliste Prieto, José, Zamora, José
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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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Chromatic Symmetric Functions and RSK for (3+1)-Free Posets
, 2023 In 1995, Stanley introduced the chromatic symmetric function of a graph, a symmetric function analog of the classical chromatic polynomial of a graph.
Celano, Kyle
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