Enumeration of 0/1-matrices avoiding some 2x2 matrices

TL;DR

This paper counts 0/1-matrices that do not contain certain 2x2 submatrices and derives their exponential generating functions, advancing combinatorial enumeration techniques.

Contribution

It introduces a systematic enumeration method for 0/1-matrices avoiding specific 2x2 patterns and provides explicit generating functions.

Findings

Derived formulas for the number of matrices avoiding given 2x2 submatrices

Provided exponential generating functions for these classes

Enhanced understanding of pattern-avoiding matrix enumeration

Abstract

We enumerate the number of 0/1-matrices avoiding 2x2 submatrices satisfying certain conditions. We also provide corresponding exponential generating functions.