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Formulas for the expansion of arbitrary invariant group functions in terms of the characters for the Sp(2N), SO(2N+1), and SO(2N) groups are derived using a combinatorial method. The method is similar to one used by Balantekin to expand…

We introduce and systematically study linear sofic groups and linear sofic algebras. This generalizes amenable and LEF groups and algebras. We prove that a group is linear sofic if and only if its group algebra is linear sofic. We show that…

We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics.…

We consider eventually positive operator semigroups and study the question whether their eventual positivity is preserved by bounded perturbations of the generator or not. We demonstrate that eventual positivity is not stable with respect…

In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.

It is proved that each of compact linear groups of one special type admits a semialgebraic continuous factorization map onto a real vector space.

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…

Any continuous piecewise-linear function $F\colon \mathbb{R}^{n}\to \mathbb{R}$ can be represented as a linear combination of $\max$ functions of at most $n+1$ affine-linear functions. In our previous paper [``Representing piecewise linear…

We develop a formalism to extract triple crossing symmetric positivity bounds for effective field theories with multiple degrees of freedom, by making use of $su$ symmetric dispersion relations supplemented with positivity of the partial…

Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…

Some polynomials $P$ with rational coefficients give rise to well defined maps between cyclic groups, $\Z_q\longrightarrow\Z_r$, $x+q\Z\longmapsto P(x)+r\Z$. More generally, there are polynomials in several variables with tuples of rational…

We provide a complete combinatorial and asymptotic analysis of positive linear systems of equations in one catalytic variable that appear in several combinatorial problems such as in lattice path counting or stack-sortable permutation…

We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of Horodecki Theorem, giving a necessary and sufficient criterion for…

We prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous…

Functional equations with one catalytic appear in several combinatorial applications, most notably in the enumeration of lattice paths and in the enumeration of planar maps. The main purpose of this paper is to show that under certain…

A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a…

Suppose that a binary operation $\circ$ on a finite set $X$ is injective in each variable separately and also associative. It is easy to prove that $(X,\circ)$ must be a group. In this paper we examine what happens if one knows only that a…

The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.

We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their…