On a conjecture concerning enumeration of 2n x k n-times persymmetric matrices over F_2 by rank

TL;DR

This paper discusses a conjecture related to counting n-times persymmetric matrices over the finite field F_2 based on their rank, aiming to advance understanding in matrix enumeration.

Contribution

It introduces a new conjecture on the enumeration of 2n x k n-times persymmetric matrices over F_2 by rank, proposing a novel theoretical insight.

Findings

Conjecture proposed for counting matrices by rank.

Potential framework for future proofs and enumeration methods.

Advances understanding of matrix structures over finite fields.

Abstract

In this paper we announce a conjecture concerning enumeration of 2n x k n-times persymmetric matrices over F_2 by rank.