Constrained Underdiagonal Paths and Pattern Avoiding Permutations
Year: 2025
Type: article
Abstract: Moving from a simple bijection P between permutations Sn of length n and underdiagonal paths of size n, The we study and enumerate families of underdiagonal paths which are defined by restricting the bijection P to subclasses of Sn avoiding some vincular patterns. In particular, we will consider patterns of lengths 3 and 4, and, when it is possible, we will provide a characterization of the underdiagonal paths related to them in terms of geometrical constraints, or equivalently, the avoidance of some factors. Finally, we will provide a recursive growth of these families by means of generating trees and then their enumerative sequence.
Source: Mathematics
DOI: 10.3390/math13030517
Institutions: University of Florence, University of Pisa, University of Siena
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4407140803