Related papers: Extending a word property for twisted Coxeter syst…

The cyclically reduced product of two words $u, v$, denoted $u * v$, is the cyclically reduced form of the concatenation of $u$ by $v$. This product is not associative. Recently S. V. Ivanov has proved that the Andrews-Curtis conjecture can…

We reinterpret an inequality, due originally to Sidorenko, for linear extensions of posets in terms of convex subsets of the symmetric group $\mathfrak{S}_n$. We conjecture that the analogous inequalities hold in arbitrary…

It is well known that many geometric properties of Schubert varieties of type $A$ can be interpreted combinatorially. Given two permutations $w,x\in S_n$ we give a combinatorial consequence of the property that the smooth locus of the…

We introduce quasi-Prufer extensions of rings in order to relativize the notion of quasi-Prufer domains and to take into account some contexts recently introduced in the literature. We also introduce almost-Prufer ring extensions.…

Let $k$ be a field. Let $A$ and $B$ be connected $N$-graded $k$-algebras. Let $C$ denote a twisted tensor product of $A$ and $B$ in the category of connected $N$-graded $k$-algebras. The purpose of this paper is to understand when $C$…

Let $(W,S)$ be any Coxeter system and let $w \mapsto w^*$ be an involution of $W$ which preserves the set of simple generators $S$. Lusztig and Vogan have shown that the corresponding set of twisted involutions (i.e., elements $w \in W$…

Hoffstein and Hulse defined the shifted convolution series of two cusp forms by "shifting" the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harmonic Maass forms to study the behavior in h-aspect of…

We prove refined generating series formulae for characters of (virtual) cohomology representations of external products of suitable coefficients, e.g., (complexes of) constructible or coherent sheaves, or (complexes of) mixed Hodge modules…

Word order evolution has been hypothesized to be constrained by a word order permutation ring: transitions involving orders that are closer in the permutation ring are more likely. The hypothesis can be seen as a particular case of…

We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…

A right-angled Coxeter group is a group with a given set of generators of order two, subject only to the relations that certain pairs of the generators commute. Various papers have shown how homological properties of the Coxeter group are…

We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.

In this paper, we study the twist-conjecture for Coxeter systems and rigidity of Coxeter systems up to finite twists. For Coxeter systems $(W,R)$ and $(W,S)$, under the untangle-condition for conjugate subsets, we investigate separations…

We introduce the notion of expandability in the context of automaton semigroups and groups: a word is k-expandable if one can append a suffix to it such that the size of the orbit under the action of the automaton increases by at least k.…

Verification of properties expressed as-regular languages such as LTL can benefit hugely from stutter-insensitivity, using a diverse set of reduction strategies. However properties that are not stutter-insensitive, for instance due to the…

We define an analog of David Little's algorithm for reduced words in type B, and investigate its main properties. In particular, we show that our algorithm preserves the recording tableau of Kra\'{s}kiewicz insertion, and that it provides a…

The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin…

We establish power-saving estimates for general bilinear forms with Kloosterman sums modulo arbitrary q, including when both variables are shorter than the Polya-Vinogradov range. As an application, we obtain power-saving asymptotics for…

We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson…