Sorting with pattern-avoiding stacks : the 132-machine

Cerbai, Giulio and Claesson, Anders and Ferrari, Luca and Steingrímsson, Einar (2020) Sorting with pattern-avoiding stacks : the 132-machine. Electronic Journal of Combinatorics, 27 (3). 3.32. ISSN 1077-8926 (https://doi.org/10.37236/9642)

[thumbnail of Cerbai-etal-EJC-2020-Sorting-with-pattern-avoiding-stacks-the-132]
Preview
 Text. Filename: Cerbai_etal_EJC_2020_Sorting_with_pattern_avoiding_stacks_the_132.pdf
Final Published Version
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo
Download (392kB)| Preview

Abstract

This paper continues the analysis of the pattern-avoiding sorting machines recently introduced by Cerbai, Claesson and Ferrari (2020). These devices consist of two stacks, through which a permutation is passed in order to sort it, where the content of each stack must at all times avoid a certain pattern. Here we characterize and enumerate the set of permutations that can be sorted when the first stack is 132-avoiding, solving one of the open problems proposed by the above mentioned authors. To that end we present several connections with other well known combinatorial objects, such as lattice paths and restricted growth functions (which encode set partitions). We also provide new proofs for the enumeration of some sets of pattern-avoiding restricted growth functions and we expect that the tools introduced can be fruitfully employed to get further similar results.

ORCID iDs

Cerbai, Giulio, Claesson, Anders ORCID logoORCID: https://orcid.org/0000-0001-5797-8673, Ferrari, Luca and Steingrímsson, Einar ORCID logoORCID: https://orcid.org/0000-0003-4611-0849;
CORE (COnnecting REpositories)