Pattern 1^j0^i avoiding binary words

TL;DR

This paper investigates the enumeration and construction of binary words with a fixed number of ones that avoid a specific pattern, using succession rules and algorithms for systematic generation and filtering.

Contribution

It introduces a novel combinatorial approach employing jumping and marked succession rules to efficiently generate pattern-avoiding binary words with a fixed number of ones.

Findings

Developed an algorithm for constructing all binary words with a given number of ones avoiding the pattern.

Established a method to describe the growth of such words using succession rules.

Provided a systematic way to filter out words containing the forbidden pattern during generation.

Abstract

In this paper we study the enumeration and the construction, according to the number of ones, of particular binary words avoiding a fixed pattern. The growth of such words can be described by particular jumping and marked succession rules. This approach enables us to obtain an algorithm which constructs all binary words having a fixed number of ones and then kills those containing the forbidden pattern.