Related papers: On Chamber-regular $\tilde C_2$-Lattices

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

Lattice walks are used to model various physical phenomena. In particular, walks within Weyl chambers connect directly to representation theory via the Littelmann path model. We derive asymptotics for centrally weighted lattice walks within…

Given a semisimple group over a complete non-Archimedean field, it is well known that techniques from non-Archimedean analytic geometry provide an embedding of the corresponding Bruhat-Tits builidng into the analytic space associated to the…

A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences…

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by…

This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

Let k be a field of positive characteristic. We construct, for each dominant coweight \lambda of the standard maximal torus in the special linear group, a closed subvariety D(\lambda) of the multigraded Hilbert scheme of an affine space…

We establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy of Margulis in the case of higher rank…

We study the appearance of notable interval structures -- lattices, modular lattices, distributive lattices, and boolean lattices -- in both the Bruhat and weak orders of Coxeter groups. We collect and expand upon known results for…

This paper concerns locally finite 2-complexes $X_{m,n}$ which are combinatorial models for the Baumslag-Solitar groups $BS(m,n)$. We show that, in many cases, the locally compact group Aut($X_{m,n}$) contains incommensurable uniform…

For spherical Tits buildings of the classical types there are well-known explicit descriptions as flag complexes. Similarly for affine buildings of the classical types there are explicit constructions in terms of lattices. In this article…

It is known that in the lattice of normal extensions of the logic KTB there are unique logics of codimensions 1 and 2, namely, the logic of a single reflexive point, and the logic of the total relation on two points. A natural question…

In 2000, M. Burger and S. Mozes introduced universal groups acting on trees with a prescribed local action. We generalize this concept to groups acting on right-angled buildings. When the right-angled building is thick and irreducible of…

It is proved that if S^6 possesses an integrable complex structure, then there exists a 1-dimensional family of pairwise different exotic complex structures on P_3(C). This follows immediately from the main result of the paper: S^6 is not…

The fundamental combinatorial structure of a net in CP^2 is its associated set of mutually orthogonal latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding…

We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as…

A certain family of orthogonal groups (called "Clifford groups" by G. E. Wall) has arisen in a variety of different contexts in recent years. These groups have a simple definition as the automorphism groups of certain generalized…

We determine the primitive ideal space and hence the ideal lattice of a large class of separable groupoid C*-algebras that includes all 2-graph C*-algebras. A key ingredient is the notion of harmonious families of bisections in etale…

We completely characterize point--line configurations with $\Theta(n^{4/3})$ incidences when the point set is a section of the integer lattice. This can be seen as the main special case of the structural Szemer\'edi-Trotter problem. We also…