Results 61 to 70 of about 2,074 (148)
Parabolic Lusztig varieties and chromatic symmetric functions
, 2022 The characters of Kazhdan--Lusztig elements of the Hecke algebra over $S_n$ (and in particular, the chromatic symmetric function of indifference graphs) are completely encoded in the (intersection) cohomology of certain subvarieties of the flag variety ...
Abreu, Alex, Nigro, Antonio
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Descents, quasi-symmetric functions, and the chromatic symmetric function
, 1997 14 ...
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The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix
, 2023 We expand the chromatic symmetric functions for Dyck paths of bounce number three in the elementary symmetric function basis using a combinatorial interpretation of the inverse of the Kostka matrix studied in E\u{g}ecio\u{g}lu-Remmel (1990).
Wang, Shiyun
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A Linear Algebraic Method on the Chromatic Symmetric Function [PDF]
, 2023 The Stanley-Stembridge conjecture is a longstanding conjecture that has evaded proof for nearly 30 years. Concerned with the e-basis expansions of the chromatic symmetric functions of unit-interval graphs, this conjecture has served as a significant ...
Haithcock, Evan
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On Calculating the Chromatic Symmetric Function
This paper investigates methods for calculating the chromatic symmetric function (CSF) of a graph in chromatic-bases and the $m_λ$-basis. Our key contributions include a novel approach for calculating the CSF in chromatic-bases constructed from forests and an efficient method for determining the CSF in the $m_λ$-basis.
Mobaraki, Nima Amoei +2 more
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Chromatic quasisymmetric functions
, 2016 We introduce a quasisymmetric refinement of Stanley's chromatic symmetric function. We derive refinements of both Gasharov's Schur-basis expansion of the chromatic symmetric function and Chow's expansion in Gessel's basis of fundamental quasisymmetric ...
Shareshian, John, Wachs, Michelle L
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The Chromatic Symmetric Function of Graphs Glued at a Single Vertex
The Electronic Journal of CombinatoricsWe describe how the chromatic symmetric function of two graphs glued at a single vertex can be expressed as a matrix multiplication using certain information of the two individual graphs. We then prove new $e$-positivity results by using a connection between forest triples, defined by the first author, and Hikita's probabilities associated to standard ...
Foster Tom, Aarush Vailaya
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Splitting the cohomology of Hessenberg varieties and e-positivity of chromatic symmetric functions
, 2023 For each indifference graph, there is an associated regular semisimple Hessenberg variety, whose cohomology recovers the chromatic symmetric function of the graph.
Abreu, Alex, Nigro, Antonio
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On K-theoretic polynomials and the chromatic symmetric function
This thesis explores various problems related to polynomials from combinatorial K-theory and/or to the chromatic symmetric function. We prove four main results: 1.
Pierson, Laura
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MacMahon symmetric functions, the partition lattice, and young subgroups
, 2001 A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we show that the MacMahon symmetric functions are the generating functions for the
Rosas, Mercedes H. +2 more
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