Reference : Associative, idempotent, symmetric, and order-preserving operations on chains
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/35930
Associative, idempotent, symmetric, and order-preserving operations on chains
English
Devillet, Jimmy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Teheux, Bruno mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
In press
Order: A Journal on the Theory of Ordered Sets and its Applications
Kluwer Academic Publishers
Yes
International
0167-8094
1572-9273
Dordrecht
Netherlands
[en] associativity ; commutative semigroup ; semilattice ; nondecreasing monotonicity ; totally ordered set ; Catalan numbers ; binary tree
[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.
University of Luxembourg - UL ; Fonds National de la Recherche - FnR
Researchers
http://hdl.handle.net/10993/35930
10.1007/s11083-019-09490-7

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