Pure Core Sets of n × n Matrices over Finite Fields

2025/10/22 by Hongyu Wang, Y. H. Zhang, Wang, Hongyu +1
Computer Science · Mathematics · #15A15 #15A21 #15B33 #16S50 #Coding theory and cryptography #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2510.19235

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

This paper studies the structure of core sets under different similarity classes. We investigate the influence of factors of the minimal polynomial with different degrees on the structure of core sets. When F is a finite field of prime order, we study the upper bound on the size of a non-core set in a similarity class in M_n(F). We prove that as |F| increases, the proportion of pure core sets among subsets of M_n(F) tends to 1.

Citations

• Null ideals of sets of 3 × 3 similar matrices with irreducible characteristic polynomial

Related

• Products of Differences in Prime Order Finite Fields
• Null ideals of sets of 3 × 3 similar matrices with irreducible characteristic polynomial
• The number of matrices over \mathbbF_q with irreducible characteristic polynomial
• The structure of the core of ideals
• Similarity of Matrices over Dedekind Rings