# Determinants of generalized binary band matrices

## TL;DR

This paper derives explicit formulas for determinants of certain binary Toeplitz matrices and demonstrates their applications in counting specific permutation types.

## Contribution

It provides new explicit determinant formulas for binary Toeplitz matrices and applies them to permutation enumeration problems.

## Key findings

- Explicit determinant formulas for binary Toeplitz matrices
- Application to enumeration of even and odd permutations
- Enhanced understanding of binary matrix determinants

## Abstract

Under binary matrices we mean matrices whose entries take one of two values. In this paper, explicit formulae for calculating the determinant of some type of binary Toeplitz matrices are obtained. Examples of the application of the determinant of binary Toeplitz matrices for the enumeration of even and odd permutations of different types are given.