Results 21 to 30 of about 6,580 (165)
Hyperbolic generalized triangle groups, property (T) and finite simple quotients
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3577-3637, December 2022., 2022 Abstract We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those hyperbolic Kazhdan groups possess finite simple quotient groups of arbitrarily large rank; they constitute ...
Pierre‐Emmanuel Caprace +3 more
wiley +1 more source
Cayley and Tutte polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun's conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs.
Matjaž Konvalinka, Igor Pak
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Journal of Graph Theory, Volume 101, Issue 2, Page 210-225, October 2022., 2022 Abstract In this article, we investigate the structure of uniformly k $k$‐connected and uniformly k $k$‐edge‐connected graphs. Whereas both types have previously been studied independent of each other, we analyze relations between these two classes. We prove that any uniformly k $k$‐connected graph is also uniformly k $k$‐edge‐connected for k≤3 $k\le 3$
Frank Göring +2 more
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Arithmetic matroids and Tutte polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce the notion of arithmetic matroid, whose main example is provided by a list of elements in a finitely generated abelian group. We study the representability of its dual, and, guided by the geometry of toric arrangements, we give a ...
Michele D'Adderio, Luca Moci
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On the Tutte-Krushkal-Renardy polynomial for cell complexes [PDF]
, 2013 Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J.
Abstract Recently V. Krushkal +4 more
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Tutte Polynomials and Link Polynomials [PDF]
Proceedings of the American Mathematical Society, 1988 We show how the Tutte polynomial of a plane graph can be evaluated as the "homfly" polynomial of an associated oriented link. Then we discuss some consequences for the partition function of the Potts model, the Four Color Problem and the time complexity of the computation of the homfly polynomial.
openaire +1 more source
Enumerating conjugacy classes of graphical groups over finite fields
Bulletin of the London Mathematical Society, Volume 54, Issue 5, Page 1923-1943, October 2022., 2022 Abstract Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to their sizes.
Tobias Rossmann
wiley +1 more source
Cumulants of the q-semicircular law, Tutte polynomials, and heaps [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 The q-semicircular law as introduced by Bożejko and Speicher interpolates between the Gaussian law and the semicircular law, and its moments have a combinatorial interpretation in terms of matchings and crossings.
Matthieu Josuat-Vergès
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On the rooted Tutte polynomial [PDF]
, 1998 The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors.
King, C., Lu, W. T., Wu, F. Y.
core +3 more sources
TinyAD: Automatic Differentiation in Geometry Processing Made Simple
Computer Graphics Forum, Volume 41, Issue 5, Page 113-124, August 2022., 2022 Abstract Non‐linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second‐order derivatives are required.
P. Schmidt +4 more
wiley +1 more source