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$\alpha$-chromatic symmetric functions
Comment: Minor ...
Haglund, Jim, Oh, Jaeseong, Yoo, Meesue
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Evaluations of Hecke algebra traces at Kazhdan-Lusztig basis elements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 For irreducible characters $\{ \chi_q^{\lambda} | \lambda \vdash n\}$ and induced sign characters $\{\epsilon_q^{\lambda} | \lambda \vdash n\}$ of the Hecke algebra $H_n(q)$, and Kazhdan-Lusztig basis elements $C'_w(q)$ with $w$ avoiding the pattern 312,
Sam Clearman +3 more
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Coloring Rings in Species [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We present a generalization of the chromatic polynomial, and chromatic symmetric function, arising in the study of combinatorial species. These invariants are defined for modules over lattice rings in species.
Jacob White
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Chromatic Bases for Symmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2016 In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if $\{ G_ k \} _{k\geq 1}$ is a set of connected graphs such that $G_k$ has $k$ vertices for each $k$, then the set of all chromatic symmetric functions $\{ X_{G_ k} \} _{k\geq 1}$ generates the algebra of
Soojin Cho, Stephanie van Willigenburg
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Structure and enumeration of $(3+1)$-free posets (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 A poset is $(3+1)$-free if it does not contain the disjoint union of chains of length 3 and 1 as an induced subposet. These posets are the subject of the $(3+1)$-free conjecture of Stanley and Stembridge.
Mathieu Guay-Paquet +2 more
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The Chromatic Symmetric Function of a Graph Centred at a Vertex [PDF]
The Electronic Journal of Combinatorics, 2019 We discover new linear relations between the chromatic symmetric functions of certain sequences of graphs and apply these relations to find new families of $e$-positive unit interval graphs. Motivated by the results of Gebhard and Sagan, we revisit their ideas and reinterpret their equivalence relation in terms of a new quotient algebra of NCSym.
Farid Aliniaeifard +2 more
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A Chromatic Symmetric Function in Noncommuting Variables [PDF]
Journal of Algebraic Combinatorics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gebhard, David D., Sagan, Bruce E.
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Combinatorial reciprocity for the chromatic polynomial and the chromatic symmetric function
Discrete Mathematics, 2020 minor ...
Olivier Bernardi, Philippe Nadeau
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A note on distinguishing trees with the chromatic symmetric function [PDF]
Discrete Mathematics, 2022 For a tree $T$, consider its smallest subtree $T^{\circ}$ containing all vertices of degree at least $3$. Then the remaining edges of $T$ lie on disjoint paths each with one endpoint on $T^{\circ}$. We show that the chromatic symmetric function of $T$ determines the size of $T^{\circ}$, and the multiset of the lengths of these incident paths.
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A graph polynomial from chromatic symmetric functions
Journal of Graph Theory, 2023 AbstractMany graph polynomials may be derived from the coefficients of the chromatic symmetric function of a graph when expressed in different bases. For instance, the chromatic polynomial is obtained by mapping for each in this function, while a polynomial whose coefficients enumerate acyclic orientations is obtained by mapping for each . In this
William Chan, Logan Crew
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