Related papers: Divergence, thickness and hypergraph index for gen…

Here, for $W$ the Coxeter group $\mathrm{D}_n$ where $n > 4$, it is proved that the maximal rank of an abstract regular polytope for $W$ is $n - 1$ if $n$ is even and $n$ if $n$ is odd. Further it is shown that $W$ has abstract regular…

We further develop the theory of $W\!$-graph ideals, first introduced by the authors in reference [6]. We discuss $W\!$-graph subideals, and induction and restriction of $W\!$-graph ideals for parabolic subgroups. We introduce $W\!$-graph…

In this paper, we prove that all finitely generated malnormal subgroups of one-ended right-angled Coxeter groups are strongly quasiconvex and they are in particular quasiconvex when the ambient groups are hyperbolic. The key idea is to…

We study the (complex) Hecke algebra $\mathcal{H}_S(\mathbf{q})$ of a finite simply-laced Coxeter system $(W,S)$ with independent parameters $\mathbf{q} \in \left( \mathbb{C} \setminus\{\text{roots of unity}\} \right)^S$. We construct its…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

Let $(W,S)$ be a Coxeter system with $I\subseteq S$ such that the parabolic subgroup $W_I$ is finite. Associated to this data there is a \textit{Hecke algebra} $\scH$ and a \textit{parabolic Hecke algebra}…

We compute Aut(W) for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by removing a single vertex. The description is given explicitly in…

For a $k$-uniform hypergraph $F$ let $\textrm{ex}(n,F)$ be the maximum number of edges of a $k$-uniform $n$-vertex hypergraph $H$ which contains no copy of $F$. Determining or estimating $\textrm{ex}(n,F)$ is a classical and central problem…

This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse…

In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group W. We give a geometric characterization of the existence of a join for a subset X in W in terms of the inversion sets of its elements and…

We give explicit necessary and sufficient conditions for the abstract commensurability of certain families of 1-ended, hyperbolic groups, namely right-angled Coxeter groups defined by generalized theta-graphs and cycles of generalized…

We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We…

We develop a theory of \emph{strongly quasiconvex subgroups} of an arbitrary finitely generated group. Strong quasiconvexity generalizes quasiconvexity in hyperbolic groups and is preserved under quasi-isometry. We show that strongly…

If S and S' are two finite sets of Coxeter generators for a right-angled Coxeter group W, then the Coxeter systems (W,S) and (W,S') are equivalent.

Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…

In this paper, we prove a collection of results on graphical indices. We determine the extremal graphs attaining the maximal generalized Wiener index (e.g. the hyper-Wiener index) among all graphs with given matching number or independence…

Coxeter groups are equipped with a partial order known as the weak order, such that $u \leq v$ if the inversions of $u$ are a subset of the inversions of $v$. In finite Coxeter groups, weak order is a complete lattice, but in infinite…

In the course of investigating regular subalgebras of E(10) related to cosmological solutions of 11-dimensional supergravity supporting an electric 4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E(10) was uncovered…

Suppose that W is a finite, unitary, reflection group acting on the complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in W, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a…

For a $k$-uniform hypergraph $F$ let $\textrm{ex}(n,F)$ be the maximum number of edges of a $k$-uniform $n$-vertex hypergraph $H$ which contains no copy of $F$. Determining or estimating $\textrm{ex}(n,F)$ is a classical and central problem…