Juxtaposing Catalan permutation classes with monotone ones

2016/11/16 by Robert Brignall, Brignall, Robert, Jakub Sliačan +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Artificial intelligence #Biology #Catalan #Catalan number #Class (philosophy) #Combinatorics #Combinatorics (math.CO) #Computer science #Context (archaeology) #Cyclic permutation #Discrete mathematics #FOS: Mathematics #Geometry #Linguistics #Mathematics #Monotone polygon #Permutation (music) #Philosophy #Physics #Symmetric group #math.CO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1611.05370

17 pages

openalex publication_date 2016/11/16 · arxiv created 2017/03/28 · arxiv updated 2017/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

This paper enumerates all juxtaposition classes of the form "Av(abc) next to Av(xy)", where abc is a permutation of length three and xy is a permutation of length two. We use Dyck paths decorated by sequences of points to represent elements from such a juxtaposition class. Context-free grammars are then used to enumerate these decorated Dyck paths.

Citations

• Small permutation classes

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