Restricted Jacobi permutations
Abstract
Jacobi permutations, introduced by Viennot in the context of Jacobi elliptic functions, are counted by the Euler numbers E n appearing in the series expansion sec x + tan x = ∞ n=0 E n x n /n!.We conduct a systematic study of pattern avoidance in Jacobi permutations, achieving a complete enumeration of Jacobi permutations avoiding a prescribed set of length 3 patterns.In the case of a single pattern restriction, we obtain refined enumerations with respect to several permutation statistics: the number of ascents (or descents), the number of left-to-right minima, and the last letter.Bijections involving certain subfamilies of binary trees and Dyck paths, as well as generating function techniques, play important roles in our proofs.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Combinatorial Mathematics
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Enumerative Combinatorics and Applications
- Volume
- 7
- Issue
- 1
- Pages
- Article #S2R2–Article #S2R2
- Publication date
- 31 July 2026
- Language
- EN