Related papers: A new Menon-type identity derived from group actio…

We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-action has been considered on a strongly monotone skew-product semiflow. Here we relax the…

We describe standard forms for elements of the higher-dimensional Thompson groups $nV$ arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these…

Motivated by generalizing Szemer\'edi's theorem, we the elements in a discrete quantum group fixing a sequence of finite subsets and prove that the set of these elements is a quantum subgroup. Using this we obtain a version of mean ergodic…

A new sums-of-tails identity involving two parameters $b$ and $d$ is obtained and is used to derive more results of similar type. One of Ramanujan's sums-of-tails identities from the Lost Notebook is shown to be a special case of our…

This paper provides a bridge between two active areas of research, the spectrum (set of element orders) and the power graph of a finite group. The order sequence of a finite group $G$ is the list of orders of elements of the group, arranged…

The design of a complex system warrants a compositional methodology, i.e., composing simple components to obtain a larger system that exhibits their collective behavior in a meaningful way. We propose an automaton-based paradigm for…

In this work, we propose a new similarity index for images considering the entropy function and group theory. This index considers an algebraic group of images, it is defined by an inner law that provides a novel approach for the…

We prove a mean ergodic theorem for amenable discrete quantum groups. As an application, we prove a Wiener type theorem for continuous measures on compact metrizable groups.

This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.

A simple mathematical model is proposed to study the effect of the average trend of a population on the opinion of each individual, when a group decision has to be made by voting. It is shown that if such effect is strong enough a…

The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…

Semigroup actions and their invertible extensions are discussed. First, we develop a theory of natural extensions for continuous actions of countable, embeddable semigroups. Second, we demonstrate that not every surjective such action of 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,…

Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…

The primary tool for analysing groups acting on trees is Bass--Serre Theory. It is comprised of two parts: a decomposition result, in which an action is decomposed via a graph of groups, and a construction result, in which graphs of groups…

From an identity connecting a combinatorial sum and Legendre polynomials, we derive closed forms for a number of combinatorial sums. Some of them are obtained via results about the integrals of functions associated with Legendre…

Let $G$ be a finite group. Then we denote $\psi(G) = \sum_{x\in G}o(x)$ where $o(x)$ is the order of the element $x$ in $G$. In this paper we characterize some finite $p$-groups ($p$ a prime) by $\psi$ and their orders.

This paper enriches the list of known properties of congruence sequences starting from the universal relation and successively performing the operators lower $k$ and lower $t$. Two series of inverse semigroups, namely…

The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…

Let $\chi$ be a Dirichlet character (mod $n$) with conductor $d$. In a quite recent paper Zhao and Cao deduced the identity $\sum_{k=1}^n (k-1,n) \chi(k)= \varphi(n)\tau(n/d)$, which reduces to Menon's identity if $\chi$ is the principal…