Related papers: Reduced words for clans
We describe an algorithm to identify a minimal set of "braid relations" which span and preserve all sets of involution words for twisted Coxeter systems of finite or affine type. We classify the cases in which adding the smallest possible…
We generalize the study of standard Lyndon loop words from [A.Negut, A.Tsymbaliuk, "Quantum loop groups and shuffle algebras via Lyndon words", Adv. Math. 439 (2024), Paper No. 109482] to a more general class of orders on the underlying…
We study the problem of determining when the reduced twisted group C*-algebra associated with a discrete group G is simple and/or has a unique tracial state, and present new sufficient conditions for this to hold. One of our main tools is a…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
For commutative rings, we introduce the notion of a {\em universal grading}, which can be viewed as the "largest possible grading". While not every commutative ring (or order) has a universal grading, we prove that every {\em reduced order}…
We analyze here a particular kind of linguistic network where vertices representwords and edges stand for syntactic relationships between words. The statisticalproperties of these networks have been recently studied and various features…
Consider matrices of order $k+N$ over $p$-adic field determined up to conjugations by elements of $GL$ over $p$-adic integers. We define a product of such conjugacy classes and construct the analog of characteristic functions (transfer…
We introduce the notions of relational groupoids and relational convolution algebras. We provide various examples arising from the group algebra of a group $G$ and a given normal subgroup $H$. We also give conditions for the existence of a…
Given a reductive group scheme $G$, we give a linear algebraic description of reduced \'etale $4$-cocycles on its classifying stack $\mathrm B(G)$. These cocycles form a $2$-groupoid, which we interpret as parameters of metaplectic covers…
Stanley's formula for the number of reduced expressions of a permutation regarded as a Coxeter group element raises the question of how to enumerate the reduced expressions of an arbitrary Coxeter group element. We provide a framework for…
This paper is aimed at investigating links between Fell bundles over Morita equivalent groupoids and their corresponding reduced C*-algebras. Mainly, we review the notion of Fell pairs over a Morita equivalence of groupoids, and give the…
We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…
Given an infinite linear group with a finite set of generators, we show that the shortest word length of an element of infinite order has an upper bound that depends only on the number of generators and the degree. This provides a…
We construct a compactification of the Bruhat-Tits building associated to the group PGL(V) which can be identified with the space of homothety classes of seminorms on V endowed with the topology of pointwise convergence. Then we define a…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
In this article, we discuss the notion of partition of elements in an arbitrary Coxeter system $(W,S)$: a partition of an element $w$ is a subset $\mathcal P\subseteq W$ such that the left inversion set of $w$ is the disjoint union of the…
In this paper we explore the connections between the class of Visibly Pushdown Languages ($\mathbf{VPL}$) and the natural sets of words one can associate to a finitely generated group. We show that the word problem of a finitely generated…
We introduce a class of subshifts under the name of "standard one-counter shifts". The standard one-counter shifts are the Markov coded systems of certain Markov codes that belong to the family of one-counter languages. We study topological…
We develop the relationship between minimal transitive star factorizations and noncrossing partitions. This gives a new combinatorial proof of a result by Irving and Rattan, and a specialization of a result of Kreweras. It also arises in a…
We enlarge a Coxeter group into a category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This category, the singular Coxeter monoid, is connected to the geometry of partial flag varieties.…