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Article (Scientific journals)
Associative, idempotent, symmetric, and order-preserving operations on chains
DEVILLET, Jimmy; TEHEUX, Bruno
2020 • In Order: A Journal on the Theory of Ordered Sets and its Applications, 37 (1), p. 45-58
Peer reviewed
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https://hdl.handle.net/10993/35930
DOI
10.1007/s11083-019-09490-7
 

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Keywords :
associativity; commutative semigroup; semilattice; nondecreasing monotonicity; totally ordered set; Catalan numbers; binary tree
Abstract :
[en] We characterize the associative, idempotent, symmetric, and order-preserving operations on (finite) chains in terms of properties of (the Hasse diagram of) their associated semilattice order. In particular, we prove that the number of associative, idempotent, symmetric, and order-preserving operations on an n-element chain is the nth Catalan number.
Disciplines :
Mathematics
Author, co-author :
DEVILLET, Jimmy ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
TEHEUX, Bruno ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Associative, idempotent, symmetric, and order-preserving operations on chains
Publication date :
April 2020
Journal title :
Order: A Journal on the Theory of Ordered Sets and its Applications
ISSN :
0167-8094
eISSN :
1572-9273
Publisher :
Kluwer Academic Publishers, Dordrecht, Netherlands
Volume :
37
Issue :
1
Pages :
45-58
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
FnR Project :
FNR10949314 - Geometric And Stochastic Methods In Mathematics And Applications, 2015 (01/10/2016-31/03/2023) - Gabor Wiese
Funders :
University of Luxembourg - UL
FNR - Fonds National de la Recherche
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since 15 June 2018

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