A. Abdollahi

activity

20022023

most citedGroups all of whose undirected Cayley graphs are integral

21 citations · 87 across the 47 of their papers we have counts for

collaborators

55 papers

math.CO2023

Integral Cayley graphs of symmetric groups on transpositions

Alireza Abdollahi, Majid Arezoomand, Mahdi Ebrahimi

We study subsets $T$ consisting of some transpositions $(i, j)$ of the symmetric group $S_{n}$ on ${1, \dots, n}$ such that the Cayley graph $Γ_{T} := C a y (S_{n}, T)$ is an integral graph, i.…

math.CO2023

New Upper Bounds on the Size of Permutation Codes under Kendall $τ$ -Metric

Alireza Abdollahi, Javad Bagherian, Fatemeh Jafari +3

We first give two methods based on the representation theory of symmetric groups to study the largest size $P (n, d)$ of permutation codes of length $n$ i.e. subsets of the set $S_{n}$ …

math.GR2022

Nilpotent probability of compact groups

Alireza Abdollahi, Meisam Soleimani Malekan

Let $k$ be any positive integer and $G$ a compact (Hausdorff) group. Let $\mf{np}_k(G)$ denote the probability that $k + 1$ randomly chosen elements $x_{1}, \dots, x_{k + 1}$ satisfy $[x_1…

math.CO2022

New Bounds on the Size of Permutation Codes With Minimum Kendall $τ$ -distance of Three

A. Abdollahi, J. Bagherian, F. Jafari +3

We study $P (n, 3)$ , the size of the largest subset of the set of all permutations $S_{n}$ with minimum Kendall $τ$ -distance $3$ . Using a combination of group theory and integer progra…

math.GR2021

Commuting Probability of Compact Groups

Alireza Abdollahi, Meisam soleimani Malekan

For any (Hausdorff) compact group $G$ with the normalized Haar measure $m_{G}$ , denote by $cp (G)$ the probability ${\mathbf m}_{G\times G}(\{(x,y)\in G\times G \;|\;…

math.GR2021★ 1 cited

Compact groups with a set of positive Haar measure satisfying a nilpotent law