Bivariate local permutation polynomials, their companions, and related enumeration results

2025/02/21 by Hasan, Sartaj Ul, Kaur, Ramandeep, Kumar, Hridesh
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.15647

Abstract

We introduce two new families of permutation group polynomials over finite fields of arbitrary characteristic, which are special types of bivariate local permutation polynomials. For each family, we explicitly construct their companions. Furthermore, we precisely determine the total number of permutation group polynomials equivalent to the proposed families. Moreover, we resolve the problem of enumerating permutation group polynomials that are equivalent to e-Klenian polynomials over finite fields for e≥ 1, a problem previously noted as nontrivial by Gutierrez and Urroz (2023).

Related

• Local permutation polynomials and their companions
• Specific permutation polynomials over finite fields
• Local permutation polynomials and the action of e-Klenian groups
• A note on two classes of permutation polynomials over finite fields
• Permutation and local permutation polynomial of maximum degree