Constrained Underdiagonal Paths and Pattern Avoiding Permutations

Andrea Frosini (), Veronica Guerrini and Simone Rinaldi
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Andrea Frosini: Department of Mathematics and Informatics, University of Firenze, 50141 Florence, Italy
Veronica Guerrini: Department of Informatics, University of Pisa, 56127 Pisa, Italy
Simone Rinaldi: Department of Information Engineering and Mathematics, University of Siena, 53100 Siena, Italy

Mathematics, 2025, vol. 13, issue 3, 1-19

Abstract: Moving from a simple bijection P between permutations S n 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 S n 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.

Keywords: pattern avoiding permutations; inversion sequences; lattice paths; generating trees (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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