# Hasan ArslanErciyes Üniversitesi · Department of Mathematics

Hasan Arslan

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20

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Introduction

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## Publications

Publications (20)

This paper is a continuation of earlier work of Arslan \cite{Ars}, who introduced the Mahonian number of type $B$ by using a new statistic on the hyperoctahedral group $B_{n}$, in response to questions he suggested in his paper entitled "{\it A combinatorial interpretation of Mahonian numbers of type $B$}" published in arXiv:2404.05099v1. We first...

The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the category of soft groups is a symmetric monodial category.

In this paper, we introduce an inversion statistic on the hyperoctahedral group $B_n$ by using an decomposition of a positive root system of this reflection group. Then we prove some combinatorial properties for the inversion statistic. We establish an enumeration system on the group $B_n$ and give an efficient method to uniquely derive any group e...

In this paper, we construct a mixed-base number system over the generalized symmetric group G(m, 1, n), which is a complex reflection group with a root system of type B (m) n. We also establish one-to-one correspondence between all positive integers in the set {1, · · · , m n n!} and the elements of G(m, 1, n) by constructing the subexceedant funct...

In this paper, our main objective is to combinatorially obtain all characteristic class functions of the Weyl group of type G_2 with the help of the structure of generalized descent algebra including Solomon’s descent algebra and Mantaci-Reutenauer algebra. We also give an interpretation of the character table of the Weyl group of type G_2 in terms...

In this paper, we construct a mixed-base number system over a complex reflection group $G(m,1,n)$, the generalized symmetric group. We also introduce one-to-one correspondence between positive integers and elements of $G(m,1,n)$ after constructing the subexceedant function in relation to this group.

In this paper, we define a mixed-base number system over a Weyl group of type $D$, the group even-signed permutations. We introduce one-to-one correspondence between positive integers and elements of Weyl groups of type $D$ after constructed the subexceedant function associating to the group. Thus, the integer representations of all classical Weyl...

A novel coronavirus SARS-CoV-2, a pathogenic single-stranded positive sense RNA virus, emerged in China in late December 2019 and spread rapidly throughout the world. The SARS-CoV-2 virus, which is genetically similar to SARS-CoV, caused a severe illness known as COVID-19 disease and a serious number of deaths worldwide (1,410,378 deaths as of Nov...

The main aim of this work is to give a case-free algebraic proof for a theorem of Eng on the Poincaré polynomial of parabolic quotients of finite Coxeter groups evaluated at -1.

Various viral epidemics have been detected such as the severe acute respiratory syndrome coronavirus and the Middle East respiratory syndrome coronavirus in the last two decades. The coronavirus disease 2019 (COVID-19) is a pandemic caused by a novel betacoronavirus called severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). After the rapi...

The main aim of this work is to introduce the Gaussian Pell quaternion QGpn and Gaussian Pell-Lucas quaternion QGqn, where the components of QGpn and QGqn are Pell numbers pn and Pell-Lucas numbers qn, respectively. Firstly, we obtain the recurrence relations and Binet formulas for QGpn and QGqn. We use Binet formulas to prove Cassini?s identity fo...

The main aim of this work is to introduce the complex Gaussian Jacobsthal and Jacobsthal-Lucas quaternions and investigate their structures. We obtain the recurrence relations, Binet formulas and generating functions for these quaternions. We also give their Cassini identities by using Binet formulas. Furthermore, we prove some results for these qu...

The main aim of this work is to give a case-free algebraic proof for a theorem of Eng on the Poincar\'e polynomial of parabolic quotients of finite Coxeter groups evaluated at -1.

In this paper, we have first presented the construction of the linear characters of a finite Coxeter group Gn of type Bn by lifting all linear characters of the quotient group Gn∉[Gn, Gn] of the commutator subgroup [Gn, Gn]. Also we show that the sets of distinguished coset representatives DA and DA′ for any two signed compositions A, A′ of n which...

We define the generalized Burnside algebra $HB(W_{n})$ for $B_{n}$-type
Coxeter group $W_{n}$ and construct an surjective algebra morphism between
Mantaci-Reutenauer algebra ${\sum}'(W_{n})$ and $HB(W_{n})$. Then, by obtaining
the primitive idempotents $(e_{\lambda})_{\lambda \in \mathcal{DP}(n)}$ of
$HB(W_{n})$, we consider the image $\textrm{res}...