Results 51 to 60 of about 568,566 (214)
Ultimate chromatic polynomials
Discrete Mathematics, 1994 An approach to enumeration problems relying on the algebra of free abelian groups is outlined. The main application is a generalization of the chromatic polynomial of a simple graph \(G\) to the ``ultimate chromatic polynomial'', which lies in the free abelian group generated by the poset \(K(G)\) of contractions of \(G\), and which reduces to the ...
Nigel Ray, William Schmitt
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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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Macdonald Polynomials and Chromatic Quasisymmetric Functions [PDF]
Electronic Journal of Combinatorics, 2017 We express the integral form Macdonald polynomials as a weighted sum of Shareshian and Wachs' chromatic quasisymmetric functions of certain graphs.
J. Haglund, A. Wilson
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Boundary Chromatic Polynomial [PDF]
Journal of Statistical Physics, 2008 We consider proper colorings of planar graphs embedded in the annulus, such that vertices on one rim can take Q_s colors, while all remaining vertices can take Q colors. The corresponding chromatic polynomial is related to the partition function of a boundary loop model. Using results for the latter, the phase diagram of the coloring problem (with real
Jacobsen, Jesper Lykke, Saleur, Hubert
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An equivalent formulation of chromatic quasi-polynomials [PDF]
Discrete Mathematics, 2018 Given a central integral arrangement, the reduction of the arrangement modulo a positive integer q gives rise to a subgroup arrangement in Z q l . Kamiya et al.
T. Tran
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The limit of chromatic polynomials
Journal of Combinatorial Theory, Series B, 1979 AbstractWe consider the large size limit of the number of q-colourings for three types of planar graph and obtain expansions for this limit in powers of (q − 1)−1. The methods used to derive and investigate these series are related to more general methods of investigating the Tutte polynomial used in theoretical physics.
D. Kim, Ian G. Enting
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Angewandte Chemie, EarlyView.Color‐pure all‐organic emitters, i.e., with narrow spectral characteristics, are intensively studied for high‐definition organic LEDs and multi‐color bioimaging. In order to guide targeted materials design, this educative review discusses spectral characteristics, proper definitions and units, and the physical basis of spectral broadening, to distill ...
Johannes Gierschner +6 more
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The chromatic polynomial of a graph [PDF]
Pacific Journal of Mathematics, 1985 First, the author summarizes some known results on chromatical polynomials and sketches their proofs. Then he lists the chromatical polynomials of all graphs with fewer than seven vertices.
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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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On Weak Chromatic Polynomials of Mixed Graphs [PDF]
Graphs Comb., 2012 A mixed graph is a graph with directed edges, called arcs, and undirected edges. A k-coloring of the vertices is proper if colors from {1, 2, . . . , k} are assigned to each vertex such that u and v have different colors if uv is an edge, and the color ...
M. Beck +4 more
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