Results 11 to 20 of about 1,406 (208)
$H$-Chromatic Symmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2022 We introduce $H$-chromatic symmetric functions, $X_{G}^{H}$, which use the $H$-coloring of a graph $G$ to define a generalization of Stanley's chromatic symmetric functions. We say two graphs $G_1$ and $G_2$ are $H$-chromatically equivalent if $X_{G_1}^{H} = X_{G_2}^{H}$, and use this idea to study uniqueness results for $H$-chromatic symmetric ...
Nancy Mae Eagles +4 more
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Characters and Chromatic Symmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2021 Let $P$ be a poset, $\mathrm{inc}(P)$ its incomparability graph, and $X_{\mathrm{inc}(P)}$ the corresponding chromatic symmetric function, as defined by Stanley in Adv. Math., 111 (1995) pp.166–194. Let $\omega$ be the standard involution on symmetric functions.
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Hecke algebra and quantum chromatic symmetric functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We evaluate induced sign characters of $H_n(q)$ at certain elements of $H_n(q)$ and conjecture an interpretation for the resulting polynomials as generating functions for $P$-tableaux by a certain statistic.
Brittany Shelton, Mark Skandera
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Plethysms of Chromatic and Tutte Symmetric Functions
The Electronic Journal of Combinatorics, 2022 Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients of Schur function plethysms is a major open question. In this paper, we introduce a graph-theoretic interpretation for any plethysm
Spirkl, Sophie, Crew, Logan
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Proper q-caterpillars are distinguished by their Chromatic Symmetric Functions
Discrete Mathematics, 2023 Stanley's Tree Isomorphism Conjecture posits that the chromatic symmetric function can distinguish non-isomorphic trees. While already established for caterpillars and other subclasses of trees, we prove the conjecture's validity for a new class of trees that generalize proper caterpillars, thus confirming the conjecture for a broader class of trees.
Sagar S Sawant
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Formal Group Laws and Chromatic Symmetric Functions of Hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 If $f(x)$ is an invertible power series we may form the symmetric function $f(f^{-1}(x_1)+f^{-1}(x_2)+...)$ which is called a formal group law. We give a number of examples of power series $f(x)$ that are ordinary generating functions for combinatorial ...
Jair Taylor
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A rooted variant of Stanley's chromatic symmetric function
Discrete Mathematics, 2023 21 pages; v2: added a short algebraic proof to Theorem 2 (now Theorem 15), we also answer a question of Pawlowski about monomial expansions; v3: added additional one-variable specialization results, simplified main ...
Nicholas A Loehr, Gregory S Warrington
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A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function [PDF]
The Electronic Journal of Combinatorics, 2021 This paper has two main parts. First, we consider the Tutte symmetric function XB, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of XB and show that this function admits a deletion-contraction relation.
José Aliste-Prieto +3 more
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Chromatic quasisymmetric functions and noncommutative 𝑃-symmetric functions
Transactions of the American Mathematical SocietyFor a natural unit interval order P P , we describe proper colorings of the incomparability graph of
Hwang, Byung-Hak
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Proper caterpillars are distinguished by their chromatic symmetric function
Discrete Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
JOSÉ Aliste-Prieto, JOSÉ Zamora
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