Work

Flip-sort and combinatorial aspects of pop-stack sorting

Year: 2021

Type: article

Abstract: Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structural, enumerative, and algorithmic results on permutations that need few (resp. many) iterations of this procedure to be sorted. In particular, we give the shape of the permutations after one iteration, and characterize several families of permutations related to the best and worst cases of flip-sort. En passant, we also give some links between pop-stack sorting, automata, and lattice paths, and introduce several tactics of bijective proofs which have their own interest.

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.6196

Authors: Andrei Asinowski, Cyril Banderier, Benjamin Hackl

Institutions: University of Klagenfurt, Université Sorbonne Paris Nord

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Austrian Science Fund

Award: Analytic Combinatorics: Digits, Automata and Trees