6533b81ffe1ef96bd1277373
RESEARCH PRODUCT
Generalized Schröder permutations
Vincent VajnovszkiElena Barcuccisubject
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_MISCELLANEOUSMathematicsdescription
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].
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-09-02 |