Generation of binary words avoiding alternating patterns

TL;DR

This paper presents an algorithm to generate all binary words with a fixed number of 1's, avoiding specific alternating patterns, and proves its exhaustiveness.

Contribution

The paper introduces a novel algorithm that exhaustively generates binary words with constraints on pattern avoidance and fixed number of 1's.

Findings

Algorithm is exhaustive in generating all such binary words

All generated words avoid the pattern $(10)^j1$ for any fixed $j \\geq 1$

The method ensures no valid words are missed

Abstract

In this paper we propose an algorithm to generate binary words with no more 0's than 1's having a fixed number of 1's and avoiding the pattern $(10)^j1$ for any fixed $j \geq 1$. We will prove that this generation is exhaustive, that is, all such binary words are generated.