Restricted ascent sequences and catalan numbers

David Callan; Toufik Mansour; Mark Shattuck

doi:10.2298/AADM140626007C

Restricted ascent sequences and catalan numbers

David Callan, Toufik Mansour, Mark Shattuck

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we identify all members of the (4,4)-Wilf equivalence class for ascent sequences corresponding to the Catalan number C_n = 1/n+1(2n/n). This extends recent work concerning avoidance of a single pattern and pro-vides apparently new combinatorial interpretations for Cn. In several cases, the subset of the class consisting of those members having exactly m ascents is given by the Narayana number N_n,m+1 = 1/n(n/m+1)(n/m). We conclude by considering a further refinement in the case of avoiding 021.

Original language	American English
Pages (from-to)	288-303
Number of pages	16
Journal	Applicable Analysis and Discrete Mathematics
Volume	8
Issue number	2
DOIs	https://doi.org/10.2298/AADM140626007C
State	Published - 2014

Keywords

Ascent sequence
Catalan number
Kernel method
Narayana number

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.2298/AADM140626007C

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AU - Mansour, Toufik

AU - Shattuck, Mark

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AB - In this paper, we identify all members of the (4,4)-Wilf equivalence class for ascent sequences corresponding to the Catalan number Cn = 1/n+1(2n/n). This extends recent work concerning avoidance of a single pattern and pro-vides apparently new combinatorial interpretations for Cn. In several cases, the subset of the class consisting of those members having exactly m ascents is given by the Narayana number Nn,m+1 = 1/n(n/m+1)(n/m). We conclude by considering a further refinement in the case of avoiding 021.

KW - Ascent sequence

KW - Catalan number

KW - Kernel method

KW - Narayana number

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JO - Applicable Analysis and Discrete Mathematics

JF - Applicable Analysis and Discrete Mathematics

IS - 2

ER -

Restricted ascent sequences and catalan numbers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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