arXiv subjects

Ali Reza Moghaddamfar

Publications and source records attributed to Ali Reza Moghaddamfar.

3 recordsLinked to original sources

arXiv2026

Factorizations of Matrices With Recursive Entries and Related Topics

This article examines matrices whose entries are determined by recursive relations of the form $A_{i, j} = x A_{i, j-1} + y A_{i-1, j-1} + z A_{i-1, j}$, where $x, y, z$ are constants, and the initial conditions are defined along the first row and column. We present a general decomposition for such matrices and show that many of the known decompositions are particular cases of this more general decomposition. Additionally, we provide a decomposition of these matrices into Pascal-like matrices and a basic Toeplitz matrix.

math.CO↗

arXiv2018

Group Partitions via Commutativity and Related Topics

Let $G$ be a nonabelian group, $A\subseteq G$ an abelian subgroup and $n\geqslant 2$ an integer. We say that $G$ has an $n$-abelian partition with respect to $A$, if there exists a partition of $G$ into $A$ and $n$ disjoint commuting subsets $A_1, A_2, \ldots, A_n$ of $G$, such that $|A_i|>1$ for each $i=1, 2, \ldots, n$. We first classify all nonabelian groups, up to isomorphism, which have an $n$-abelian partition for $n=2, 3$. Then, we provide some formulas concerning the number of spanning trees of commuting graphs associated with certain finite groups. Finally, we point out some ways to finding the number of spanning trees of the commuting graphs of some specific groups.

math.GR↗

arXiv2017

On Alternating and Symmetric Groups Which Are Quasi OD-Characterizable

Let $Γ(G)$ be the prime graph associated with a finite group $G$ and $D(G)$ be the degree pattern of $G$. A finite group $G$ is said to be $k$-fold OD-characterizable if there exist exactly $k$ non-isomorphic groups $H$ such that $|H|=|G|$ and $D(H)=D(G)$. The purpose of this article is twofold. First, it shows that the symmetric group $S_{27}$ is $38$-fold OD-charaterizable. Second, it shows that there exist many infinite families of alternating and symmetric groups, $\{A_n\}$ and $\{S_n\}$, which are $k$-fold OD-characterizable with $k>3$.

math.GR↗