학술논문
Patterns in inversion sequences II: inversion sequences avoiding triples of relations.
Document Type
Journal
Author
Martinez, Megan (1-ITHC) AMS Author Profile; Savage, Carla (1-NCS-C) AMS Author Profile
Source
Subject
05 Combinatorics -- 05A Enumerative combinatorics
05A15Exact enumeration problems, generating functions
05A19Combinatorial identities, bijective combinatorics
05A15
05A19
Language
English
Abstract
This paper is a comprehensive study of pattern avoidance in inversion sequences. An {\it inversion sequence} is an integer sequence $(e_1,e_2,\ldots,e_n)$ satisfying $0\leq e_i,\leq,\geq,=,\not=,-\}$ and derive results on the set of integer sequences that avoid the given pattern, and the enumeration sequence that enumerates these sets. The results include several known sequences, such as Fibonacci numbers, Bell numbers, Catalan numbers, etc., but also many new sequences. Moreover, the authors highlight a number of conjectures and interesting open problems. \par \{For Part I see [S. Corteel et al., Discrete Math. Theor. Comput. Sci. {\bf 18} (2016), no.~2, Paper No. 2; MR3548801].\}