Search results for "Integer sequence"

showing 3 items of 3 documents

Generalized Schröder permutations

2013

We give the generating function for the integer sequence enumerating a class of pattern avoiding permutations depending on two parameters: m and p. The avoided patterns are the permutations of length m with the largest element in the first position and the second largest in one of the last p positions. For particular instances of m and p we obtain pattern avoiding classes enumerated by Schroder, Catalan and central binomial coefficient numbers, and thus, the obtained two-parameter generating function gathers under one roof known generating functions and expresses new ones. This work generalizes some earlier results of Barcucci et al. (2000) [2], Kremer (2000) [5] and Kremer (2003) [6].

Discrete mathematicsClass (set theory)General Computer Science010102 general mathematicsGenerating functionInteger sequence0102 computer and information sciences[ MATH.MATH-CO ] Mathematics [math]/Combinatorics [math.CO]01 natural sciencesTheoretical Computer ScienceCombinatorics010201 computation theory & mathematicsPosition (vector)[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]Central binomial coefficient0101 mathematicsElement (category theory)ComputingMilieux_MISCELLANEOUSMathematics
researchProduct

Catalan words avoiding pairs of length three patterns

2021

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 kn…

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
researchProduct

On the packing sums of pairs

1993

Abstract This paper is concerned with the determination of the length of the largest interval of consecutive integers of the set hA k , where A k is a sequence of integers which is a B h -sequence.

Set (abstract data type)CombinatoricsSequenceInteger sequenceInterval (graph theory)Electrical and Electronic EngineeringSafety Risk Reliability and QualityCondensed Matter PhysicsAlgorithmAtomic and Molecular Physics and OpticsSurfaces Coatings and FilmsElectronic Optical and Magnetic MaterialsMathematicsMicroelectronics Reliability
researchProduct