Msapato, D orcid.org/0000-0001-9376-4648 (2022) Modular Fuss-Catalan numbers. Discrete Mathematics, 345 (2). 112704. ISSN 0012-365X
Abstract
The modular Catalan numbers Ck,n , introduced by Hein and Huang in 2016 count equivalence classes of parenthesizations of x0 ∗ · · · ∗ xn , where ∗ is a binary k associative operation and k is a positive integer. The classical notion of associativity coincides with 1-associativity, in which case C1,n = 1 and the single 1-equivalence class has size given by the Catalan number Cn . In this paper we introduce modular Fuss-Catalan numbers C m k,n which count k-equivalence classes of parenthesizations of x0 ∗ · · · ∗ xn where ∗ is an m-ary k-associative operation for m ≥ 2. Our main results are, an explicit formula for C m k,n , and a characterisation of k-associativity.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Elsevier B.V. This is an author produced version of an article published in Discrete Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Fuss-Catalan numbers, Modular Catalan numbers, m-Dyck paths, m-ary trees, Tamari lattice, m-ary operations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Nov 2021 15:47 |
Last Modified: | 18 Mar 2023 01:37 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.disc.2021.112704 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:180224 |