On a conjecture regarding enumeration of n-times persymmetric matrices over F_2 by rank

TL;DR

This paper presents a conjecture about counting n-times persymmetric matrices over F_2 based on rank, supported by verified formulas for small values of n.

Contribution

It introduces a new conjecture on the enumeration of n-times persymmetric matrices over F_2 by rank, extending known cases.

Findings

Formulas verified for n=1, 2, 3

Conjecture proposed for general n

Supports enumeration of matrices by rank over F_2

Abstract

In this paper we announce a conjecture concerning enumeration of n-times persymmetric matrices over F_2 by rank. To justify our statement we remark that the formulas obtained are valid for n equal to one, two and three.