Generating Trees Unifying Several Classes of Four-Letter Pattern-Avoiding Descent Sequences
Year: 2026
Type: article
Abstract: A descent sequence is a word of nonnegative integers satisfying that the first term is zero, and each subsequent term is at most one plus the number of descents among the preceding terms, where a descent is a position at which a term is greater than the term immediately following it. In this work, we study descent sequences subject to the additional restriction of avoiding a given pattern of length four. We analyze seven distinct avoidance classes and provide enumerative results for each of them. Our approach is based on the construction of generating trees with one or two labels, from which we derive succession rules and corresponding systems of recurrence relations. These recurrences are then used to compute explicit generating functions for the number of descent sequences of length n avoiding either 0001, 0010, 0011, 0012, 0021, 0110, 0112, 0123, or 0132.
Source: Axioms
Author: Toufik Mansour
Institution: University of Haifa
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7164921136
FWCI:
Cites:
Cited by:
Related to: