Results 71 to 80 of about 2,074 (148)
Chromatic symmetric functions and change of basis
Algebraic CombinatoricsWe prove necessary conditions for certain elementary symmetric functions, e λ , to appear with nonzero coefficient in Stanley’s chromatic symmetric function as well as in the ...
Sagan, Bruce E., Tom, Foster
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Exploring Graphs and Chromatic Symmetric Functions [PDF]
We consider graphs with a small number of vertices and analyze the coefficients of hook partitions of their chromatic symmetric function, which is a generalization of the chromatic polynomial of a graph.
Payne, Olivia
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e-basis Coefficients of Chromatic Symmetric Functions
, 2022 A well-known result of Stanley's shows that given a graph $G$ with chromatic symmetric function expanded into the basis of elementary symmetric functions as $X_G = \sum c_{\lambda}e_{\lambda}$, the sum of the coefficients $c_{\lambda}$ for $\lambda$ with
Zhang, Yongxing, Crew, Logan
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Positivity for Stanley's chromatic functions
, 2016 This dissertation is dedicated to the study of positivity phenomena for the coefficients of the chromatic symmetric function of a graph. This function was introduced by Stanley in 1995 as a generalization of the chromatic polynomial of a graph.
Paunov, Alexander
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The Kneser chromatic function distinguishes trees
R.P. Stanley defined a invariant for graphs called the chromatic symmetric function and conjectured it is complete invariant for trees. Miezaki et al.
Nishimura, Yusaku
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Chromatic MacMahon symmetric functions of graphs
12 ...
Martin, Jeremy L., Trist, May B.
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Chromatic Quasisymmetric Function Evaluated at q=-1
Shareshian and Wachs have shown that the chromatic quasisymmetric function of the natural unit interval graph is symmetric (Shareshian--Wachs, 2016).
Liu, Yanru
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The Chromatic Symmetric Function for Unicyclic Graphs
Motivated by the question of which structural properties of a graph can be recovered from the chromatic symmetric function (CSF), we study the CSF of connected unicyclic graphs. While it is known that there can be non-isomorphic unicyclic graphs with the same CSF, we find experimentally that such examples are rare for graphs with up to 17 vertices.
Bingham, Aram +5 more
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On Chromatic Quasisymmetric Functions of Directed Graphs
, 2018 In 1912, Birkhoff introduced the chromatic polynomial of a graph, which counts the number of proper colorings of a graph. In 1995, Stanley introduced the chromatic symmetric function of a graph, a symmetric function analog of the chromatic polynomial of ...
Ellzey, Brittney
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Chromatic quasisymmetric functions of digraphs [PDF]
The chromatic quasisymmetric function of a digraph is a quasisymmetric function associated with the digraph that describes some of its properties. It generalizes the chromatic symmetric function of the graph, which generalizes the chromatic polynomial of
Fusco, Giacomo
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