Fibonacci sequence related to a combinatorial problem on binary matrices

TL;DR

This paper explores a combinatorial problem involving binary matrices with equal row and column sums, revealing new integer sequences related to Fibonacci numbers and establishing novel relationships between matrix parameters and Fibonacci sequence values.

Contribution

It introduces new integer sequences associated with binary matrices and uncovers a novel connection between these sequences and Fibonacci numbers.

Findings

New integer sequences not listed in OEIS

Relationship between matrix parameters and Fibonacci sequence

Initial values of sequences related to binary matrices

Abstract

We discuss an equivalence relation on the set of square binary matrices with the same number of 1's in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of integer sequences related to the discussed problem. The obtained sequences are new and they are not described in the On-Line Encyclopedia of Integer Sequences (OEIS). We show a relationship between some particular values of the parameters and the Fibonacci sequence.