6533b7d6fe1ef96bd12671e0

RESEARCH PRODUCT

Catalan and Schröder permutations sortable by two restricted stacks

Giulio CerbaiVincent VajnovszkiJean-luc BarilCarine Khalil

subject

Mathematics::CombinatoricsSeries (mathematics)010102 general mathematicsSortingContext (language use)0102 computer and information sciences01 natural scienceslanguage.human_languageComputer Science ApplicationsTheoretical Computer ScienceCatalan numberCombinatorics[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]Stack (abstract data type)010201 computation theory & mathematicsSymmetric groupSignal Processing[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]languageBinomial transformCatalan0101 mathematicsComputingMilieux_MISCELLANEOUSInformation SystemsMathematics

description

Abstract Pattern avoiding machines were introduced recently by Claesson, Cerbai and Ferrari as a particular case of the two-stacks in series sorting device. They consist of two restricted stacks in series, ruled by a right-greedy procedure and the stacks avoid some specified patterns. Some of the obtained results have been further generalized to Cayley permutations by Cerbai, specialized to particular patterns by Defant and Zheng, or considered in the context of functions over the symmetric group by Berlow. In this work we study pattern avoiding machines where the first stack avoids a pair of patterns of length 3 and investigate those pairs for which sortable permutations are counted by the (binomial transform of the) Catalan numbers and the Schroder numbers.

yearjournalcountryeditionlanguage
2020-06-30
https://hal.science/hal-03064500