Cyclic Pattern Containment and Avoidance

Autor:	Domagalski, Rachel, Liang, Jinting, Minnich, Quinn, Sagan, Bruce E., Schmidt, Jamie, Sietsema, Alexander
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics 05A05 (Primary) 05A15 05A19 (Secondary)
Druh dokumentu:	Working Paper
Popis:	The study of pattern containment and avoidance for linear permutations is a well-established area of enumerative combinatorics. A cyclic permutation is the set of all rotations of a linear permutation. Callan initiated the study of permutation avoidance in cyclic permutations and characterized the avoidance classes for all single permutations of length 4. We continue this work. In particular, we establish a cyclic variant of the Erdos-Szekeres Theorem that any linear permutation of length mn+1 must contain either the increasing pattern of length m+1 or the decreasing pattern of length n+1. We then derive results about avoidance of multiple patterns of length 4. We also determine generating functions for the cyclic descent statistic on these classes. Finally, we end with various open questions and avenues for future research. Comment: 23 pages, 3 figures, 1 table
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2106.02534 Zobrazit plný text záznamu View this record from Arxiv