Results 11 to 20 of about 2,074 (148)
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 class of trees determined by their chromatic symmetric functions
Discrete MathematicsStanley introduced the concept of chromatic symmetric functions of graphs which extends and refines the notion of chromatic polynomials of graphs, and asked whether trees are determined up to isomorphism by their chromatic symmetric functions. Using the technique of differentiation with respect to power-sum symmetric functions, we give a positive ...
Xingxing Yu
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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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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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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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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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The chromatic symmetric function in the star-basis
Discrete Mathematics36 pages, 8 ...
Rosa Orellana
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On Stanley's chromatic symmetric function and clawfree graphs
Discrete Mathematics, 1999 A proper coloring of a simple graph \(G\) (without loops and multiple edges) with vertex set \(V=\{v_1,\ldots,v_d\}\) is a function \(\kappa: V\to {\mathbb{N}}^+\) such that \(\kappa(u)\not=\kappa(v)\) if \(u\) and \(v\) are vertices of an edge of \(G\).
Vesselin Gasharov, Gasharov, Vesselin
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A Symmetric Function Generalization of the Chromatic Polynomial of a Graph
Advances in Mathematics, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stanley, R.P.
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