Arpan Kanrar

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math.GR2025

On Modular maximal-cyclic braces

Arpan Das, Arpan Kanrar

Inspired by a conjecture by Guarnieri and Vendramin concerning the number of braces with a generalized quaternion adjoint group, many researchers have studied braces whose adjoint…

math.GR2023

Involutive Yang-Baxter groups never act as Frobenius groups

Arpan Kanrar, Wolfgang Rump

A conjecture of S. Ram\'ırez states that every indecomposable non-degenerate involutive set-theoretic solution to the Yang-Baxter equation with dihedral permutation group of order…

math.GR2023

Cycle matrices: A combinatorial approach to the set-theoretic solutions of the Quantum Yang-Baxter Equation

Arpan Kanrar, Saikat Panja

An $n \times n$ matrix $M = [m_{ij}]$ with $m_{ij} \in U_{n} = {1, 2, \dots, n}$ will be called a cycle matrix if $(U_{n}, \cdot)$ is a cycle set, where $i \cdot j = m_{ij}$ . We study these matr…