Work

On Pattern Avoiding Indecomposable Permutations

Year: 2016

Type: preprint

Abstract: Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecomposable permutations were studied in the literature in various contexts. In particular, this notion has been proven to be useful in obtaining non-trivial enumeration and equidistribution results on permutations. In this paper, we give a complete classification of indecomposable permutations avoiding a classical pattern of length 3 or 4, and of indecomposable permutations avoiding a non-consecutive vincular pattern of length 3. Further, we provide a recursive formula for enumerating $12\cdots k$-avoiding indecomposable permutations for $k\geq 3$. Several of our results involve the descent statistic. We also provide a bijective proof of a fact relevant to our studies.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1605.05490

Authors: Gao, Alice L. L., Kitaev, Sergey, Zhang, Philip B.

Institutions: Nankai University, University of Strathclyde, Tianjin Normal University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Nankai University, Fundamental Research Funds for the Central Universities

Awards: G4613211900, G8462160042

OpenAlex ID: W2403307814

Cites:

Cited by: 8

Related to: 10