相关论文: Lattice Walks in the Octant with Infinite Associat…

This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic,…

We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs), and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of singular ASMs, with a…

We prove that the full automorphism group and the outer automorphism group of the free group of countably infinite rank are coarsely bounded. That is, these groups admit no continuous actions on a metric space with unbounded orbits, and…

Let $\Gamma$ be a non-elementary hyperbolic group and $\mu$ be a probability on $\Gamma$. We study the $\mu$-proximal, stationary actions, also known as boundary actions, of $\Gamma$. In particular, we are interested in the spectrum of…

For each of the 14 classes of edge-transitive maps described by Graver and Watkins, necessary and sufficient conditions are given for a group to be the automorphism group of a map, or of an orientable map without boundary, in that class.…

By studying connectedness at infinity of systolic groups we distinguish them from some other classes of groups, in particular from the fundamental groups of manifolds covered by euclidean space of dimension at least three. We also study…

We study several explicit finite index subgroups in the known complex hyperbolic lattice triangle groups, and show some of them are neat, some of them have positive first Betti number, some of them have a homomorphisms onto a non-Abelian…

We study lattices in free abelian groups of infinite rank that are invariant under the action of the infinite symmetric group, with emphasis on finiteness of their equivariant bases. Our framework provides a new method for proving…

We show that an adjoint of a loopless matroid is connected if and only if it itself is connected. Our first goal is to study the adjoint of modular matroids. We prove that a modular matroid has only one adjoint (up to isomorphism) which can…

We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play…

We prove that there are only finitely many closed hyperbolic 3-manifolds with injectivity radius and first eigenvalue of the Laplacian bounded below whose fundamental groups can be generated by a given number of elements. An application to…

Guided by classical concepts, we define the notion of \emph{ends} of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points…

We study a number of combinatorial and algebraic structures arising from walks on the two-dimensional integer lattice. To a given step set $X\subseteq\mathbb Z^2$, there are two naturally associated monoids: $\mathscr F_X$, the monoid of…

We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.

We study Hamiltonian walks (HWs) on the family of three--dimensional modified Sierpinski gasket fractals, as a model for compact polymers in nonhomogeneous media in three dimensions. Each member of this fractal family is labeled with an…

We propose the study of Markov chains on groups as a "quasi-isometry invariant" theory that encompasses random walks. In particular, we focus on certain classes of groups acting on hyperbolic spaces including (non-elementary) hyperbolic and…

The category $\bcalNT$ was defined in \cite{Lobos2}, it is a category whose objects are commutative nil graded algebras over a field, defined by presentation encoded by triangular matrices. A natural problem related to this category is to…

We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has been visited before. In such case the vertex is left via the…

We give a complete and irredundant list of the finite groups $G$ for which Aut$(G)$, acting naturally on $G$, has precisely $3$ orbits. There are 7 infinite families: one abelian, one non-nilpotent, three families of non-abelian $2$-groups…

We give simple examples of Kazhdan groups with infinite outer automorphism groups. This answers a question of Paulin, independently answered by Ollivier and Wise by completely different methods. As arithmetic lattices in (non-semisimple)…