Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On some classes of binary matrices

Krasimir Yordzhev

Abstract

The work considers the set $Λ_n^k$ of all $n\times n$ binary matrices having the same number of $k$ units in each row and each column. The article specifically focuses on the matrices whose rows and columns are sorted lexicographically. We examine some particular cases and special properties of this matrices. Finally, we demonstrate the relationship between the Fibonacci numbers and the cardinality of two classes of $Λ_n^k$-matrices with lexicographically sorted rows and columns.

On some classes of binary matrices

Abstract

The work considers the set of all binary matrices having the same number of units in each row and each column. The article specifically focuses on the matrices whose rows and columns are sorted lexicographically. We examine some particular cases and special properties of this matrices. Finally, we demonstrate the relationship between the Fibonacci numbers and the cardinality of two classes of -matrices with lexicographically sorted rows and columns.
Paper Structure (3 sections, 10 theorems, 47 equations)

This paper contains 3 sections, 10 theorems, 47 equations.

Table of Contents

  1. Preliminaries and notations
  2. Some properties of the sets $\Gamma_n^k$ and $\Delta_n^k$.
  3. $\Delta_n^k$ and $\Gamma_n^k$ matrices in relation to the Fibonacci numbers

Key Result

Proposition 2.1

In general,

Theorems & Definitions (19)

  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Corollary 2.1
  • Proposition 2.3
  • Corollary 2.2
  • Theorem 2.1
  • proof
  • Theorem 2.2
  • ...and 9 more