Associative, idempotent, symmetric, and order-preserving operations on chains

Devillet, Jimmy; Teheux, Bruno

doi:10.1007/s11083-019-09490-7

Reference : Associative, idempotent, symmetric, and order-preserving operations on chains


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/35930

Title :	Associative, idempotent, symmetric, and order-preserving operations on chains
Language :	English
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 >]
Publication date :	Apr-2020
Journal title :	Order: A Journal on the Theory of Ordered Sets and its Applications
Publisher :	Kluwer Academic Publishers
Volume :	37
Issue/season :	1
Pages :	45-58
Peer reviewed :	Yes
Audience :	International
ISSN :	0167-8094
e-ISSN :	1572-9273
City :	Dordrecht
Country :	Netherlands
Keywords :	[en] 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.
Funders :	University of Luxembourg - UL ; Fonds National de la Recherche - FnR
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/10993/35930
DOI :	10.1007/s11083-019-09490-7
FnR project :	FnR ; FNR10949314 > Gabor Wiese > GSM > Geometric and Stochastic Methods in Mathematics and Applications > 01/10/2016 > 31/03/2023 > 2016

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