What question did this study set out to answer?

This paper aims to explore enumerative properties of level sequences that avoid specific patterns of length three.

June 6, 2026Open Access

Wilf Classes for Level Sequences Avoiding Patterns of Length Three

Key Points

This paper aims to explore enumerative properties of level sequences that avoid specific patterns of length three.
Determined the number of Wilf equivalence classes for single patterns of length three.
Analyzed pairs of patterns of length three and extended results to sets of k patterns (3≤k≤13).
Identified the number of Wilf equivalence classes for single patterns of length 3 as well as pairs of these patterns.
Provided enumerative results for sets of k patterns, outlining specific outcomes for 3≤k≤13.

Abstract

A level sequence is a word π=π1π2…πn over the set of nonnegative integers such that π1=0 and πi≤1+lev(π1π2…πi−1) for i=2,3,…,n, where lev(π1π2…πm) is the number of levels in the word π1π2…πm, that is, the number of two entry factors πjπj+1 such that πj=πj+1. In this paper, we obtain some enumerative results for level sequences avoiding patterns of length 3. In particular, we determine the number of Wilf equivalence classes among single patterns of length 3 and among pairs of patterns of length 3, and state the corresponding result for a set of k patterns of length 3 when 3≤k≤13.

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Cite This Study

Toufik Mansour (Thu,) studied this question.

synapsesocial.com/papers/6a23b9f271a5da9775e75c74 https://doi.org/https://doi.org/10.3390/math14111983

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