6533b7d8fe1ef96bd126b808

RESEARCH PRODUCT

Descent distribution on Catalan words avoiding a pattern of length at most three

Vincent VajnovszkiJean-luc BarilSergey Kirgizov

subject

FOS: Computer and information sciencesDistribution (number theory)Discrete Mathematics (cs.DM)0102 computer and information sciences02 engineering and technologyBivariate analysis01 natural sciencesTheoretical Computer ScienceCatalan numberSet (abstract data type)Combinatorics0202 electrical engineering electronic engineering information engineeringFOS: MathematicsDiscrete Mathematics and CombinatoricsMathematics - Combinatorics[MATH]Mathematics [math]MathematicsDescent (mathematics)Discrete mathematicsGenerating functionDescent020206 networking & telecommunicationslanguage.human_languagePopularity010201 computation theory & mathematicsPattern avoidancelanguageCatalanCombinatorial classCombinatorics (math.CO)Catalan wordComputer Science - Discrete Mathematics

description

Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern $p$ we provide a bivariate generating function where the coefficient of $x^ny^k$ in its series expansion is the number of length $n$ Catalan words with $k$ descents and avoiding $p$. As a byproduct, we enumerate the set of Catalan words avoiding $p$, and we provide the popularity of descents on this set. Some of the obtained enumerating sequences are not yet recorded in the On-line Encyclopedia of Integer Sequences.

yearjournalcountryeditionlanguage
2018-09-01
http://arxiv.org/abs/1803.06706