Related papers: On coherence of graph products and Coxeter groups

In this paper we prove stability results for the homology of the mapping class group of a surface. We get a stability range that is near optimal, and extend the result to twisted coefficients.

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…

In this work, we study the $\delta$-chromatic number of a graph which is the chromatic number of the $\delta$-complement of a graph. We give a structure of the $\delta$-complements and sharp bounds on the $\delta$-chromatic numbers of the…

This note is on the structures of line graphs and 2-variegated graphs. We have given here solutions of some graph equations involving line graphs and 2-variegated graphs.

We investigate representations of Coxeter groups into $\mathrm{GL}(n,\mathbb{R})$ as geometric reflection groups which are convex cocompact in the projective space $\mathbb{P}(\mathbb{R}^n)$. We characterize which Coxeter groups admit such…

A solution of the isomorphism problem is presented for the class of Coxeter groups W that have a finite set of Coxeter generators S such that the underlying graph of the presentation diagram of the system (W,S) has the property that every…

In this short, elementary note we prove that if a faithful reflection representation of a Coxeter group preserves an orthant, then that Coxeter group is a product of symmetric groups acting on its natural permutation representation. We also…

This note is a continuation of an earlier paper by the authors. We describe improved constructions addressing a question of Erd\H{o}s and Szemer\'edi on sums and products of real numbers along the edges of a graph. We also add a few…

For vertex and edge connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.

In this paper we determine partial answers to the question given in the title, thereby significantly extending results of Broere and Hattingh. We characterize completely those pairs of complete graphs whose tensor products are circulant. We…

We study the equivalence relation on the set of acyclic orientations of an undirected graph G generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver…

The category of crossed complexes gives an algebraic model of the category of $CW$-complexes and cellular maps. We explain basic results on crossed complexes which allow the computation of free crossed resolutions of graph products of…

We prove that affine Coxeter groups, even hyperbolic Coxeter groups and one-ended hyperbolic Coxeter groups are homogeneous in the sense of model theory. More generally, we prove that many (Gromov) hyperbolic groups generated by torsion…

We show that the curvature K_(G*H)(x,y) at a point (x,y) in the strong product G*H of two arbitrary finite simple graphs is equal to the product K_G(x) K_H(y) of the curvatures.

The recently developed theory of partial actions of discrete groups on $C^*$-algebras is extended. A related concept of actions of inverse semigroups on $C^*$-algebras is defined, including covariant representations and crossed products.…

Commuting involution graphs have been studied for finite Coxeter groups and for affine groups of classical type. The purpose of this short note is to establish some general results for commuting involution graphs in affine Coxeter groups,…

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…

We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.

We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In…

This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected…