6533b829fe1ef96bd128aece

RESEARCH PRODUCT

Catalan words avoiding pairs of length three patterns

Vincent VajnovszkiCarine KhalilJean-luc Baril

subject

FOS: Computer and information sciencesMathematics::CombinatoricsDiscrete Mathematics (cs.DM)General Computer ScienceInteger sequenceBivariate analysisConstructivelanguage.human_languageTheoretical Computer ScienceCombinatorics[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]FOS: MathematicsEnumerationlanguageDiscrete Mathematics and CombinatoricsMathematics - CombinatoricsCatalanCombinatorics (math.CO)Recursive decompositionBijection injection and surjectionMathematicsDescent (mathematics)Computer Science - Discrete Mathematics

description

Catalan words are particular growth-restricted words counted by the eponymous integer sequence. In this article we consider Catalan words avoiding a pair of patterns of length 3, pursuing the recent initiating work of the first and last authors and of S. Kirgizov where (among other things) the enumeration of Catalan words avoiding a patterns of length 3 is completed. More precisely, we explore systematically the structural properties of the sets of words under consideration and give enumerating results by means of recursive decomposition, constructive bijections or bivariate generating functions with respect to the length and descent number. Some of the obtained enumerating sequences are known, and thus the corresponding results establish new combinatorial interpretations for them.

yearjournalcountryeditionlanguage
2021-04-16
https://hal.science/hal-02418787