Results 51 to 60 of about 2,074 (148)

When is the Chromatic Quasisymmetric Function Symmetric?

Algebraic Combinatorics
We investigate the problem of when a chromatic quasisymmetric function (CQF) X G ( x
Gillespie, Maria, Pappe, Joseph, Salois, Kyle   +2 more
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Chromatic Symmetric Functions of Conjoined Graphs

Frontiers of Mathematics
21 pages, 5 ...
Qi, E. Y. J., Tang, D. Q. B., Wang, D. G. L.   +2 more
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A signed \(e\)-expansion of the chromatic quasisymmetric function [PDF]

We prove a new signed elementary symmetric function expansion of the chromatic quasisymmetric function of any natural unit interval graph. We then use a sign-reversing involution to prove a new combinatorial formula for \(K\)-chains, which are graphs ...
Tom, Foster
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Bounds on the complex zeros of (Di)Chromatic polynomials and Potts-model partition functions

, 2001
We show that there exist universal constants C(r) such that, for all loopless graphs G of maximum degree less than or equal to r, the zeros (real or complex) of the chromatic polynomial P-G(q) lie in the disc \q\ 7.963907r.
Sokal, AD
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Vertex-weighted Generalizations of Chromatic Symmetric Functions

, 2020
Defined by Richard Stanley in the early 1990s, the chromatic symmetric function XG of a graph G enumerates for each integer partition λ of :V (G): the number of proper colorings of G that partition V (G) into stable sets of sizes equal to the parts of λ.
Crew, Logan, Crew, Logan Taylor
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A Noncommutative Chromatic Symmetric Function

, 1999
33 ...
Gebhard, David D., Sagan, Bruce E.
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Caterpillars, ribbons, and the chromatic symmetric function

, 2005
For every n-vertex tree T, it is known that the chromatic polynomial x(T, k) is equal to k(k — l )ⁿ⁻¹. It is known that the function in noncommuting variables, Y[sub G](x), distinguishes all simple graphs.
Morin, Matthew
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Descents, Quasi-Symmetric Functions, Robinson-Schensted for Posets, and the Chromatic Symmetric Function [PDF]

Journal of Algebraic Combinatorics, 1999
The author presents a new version of the expansion of Stanley's chromatic symmetric function [\textit{R. P. Stanley}, Discrete Math. 5, 171-178 (1973; Zbl 0258.05113)] in terms of Gessel's fundamental quasi-symmetric functions [\textit{I. M. Gessel}, Combinatorics and algebra, Proc. Conf., Boulder/Colo. 1983, Contemp. Math.
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Descents, Quasi-Symmetric Functions, Robinson-Schensted for Posets, and the Chromatic Symmetric Function

, 1997
. We investigate an apparent hodgepodge of topics: a Robinson-Schensted algorithm for (3 + 1)-free posets, Chung and Graham’s G-descent expansion of the chromatic polynomial, a quasi-symmetric expansion of the path-cycle symmetric function, and an ...
Timothy Y. Chow
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Characters and chromatic symmetric functions

, 2020
Let $P$ be a poset, $inc(P)$ its incomparability graph, and $X_{inc(P)}$ the corresponding chromatic symmetric function, as defined by Stanley in {\em Adv. Math.}, {\bf 111} (1995) pp.~166--194.

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