相关论文: General cycling operations in Garside groups

Garside groupoids, as recently introduced by Krammer, generalise Garside groups. A weak Garside group is a group that is equivalent as a category to a Garside groupoid. We show that any periodic loop in a Garside groupoid $\CG$ may be…

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a…

We provide a new combinatorial approach to studying the collection of N-infinity-operads in G-equivariant homotopy theory for G a finite cyclic group. In particular, we show that for G the cyclic group of order p^n the natural order on the…

In this paper we construct a gathering process by the means of which we obtain new normal forms in braid groups. The new normal forms generalise Artin-Markoff normal forms and possess an extremely natural geometric description. In the two…

We introduce a new tool, called the orbit automaton, that describes the action of an automaton group $G$ on the subtrees corresponding to the orbits of $G$ on levels of the tree. The connection between $G$ and the groups generated by the…

We describe new types of normal forms for braid monoids, Artin-Tits monoids, and, more generally, for all monoids in which divisibility has some convenient lattice properties (``locally Garside monoids''). We show that, in the case of…

In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…

This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.

The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian…

It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…

We explore the category of internal categories in the usual category of (right) group-sets, whose objects are referred to as categorified group-sets. More precisely, we develop a new Burnside theory, where the equivalence relation between…

The Grassmannian admits an action by a finite cyclic group via the cyclic shift map. We give a simple description of the points fixed by each element of this cyclic group, extending Karp's description of the points fixed by the cyclic shift…

For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, the zero loci of those…

We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.

Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…

As a common non-trivial generalization of the concept of a proper generalized Bassian group, we introduce the notion of a semi-generalized Bassian group and initiate its comprehensive investigation. Precisely, we give a satisfactory…

We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…

This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been…

The space of unordered configurations of distinct points in the plane is aspherical, with Artin's braid group as its fundamental group. Remarkably enough, the space of ordered configurations of distinct points on the real projective line,…