Reference : Associative, idempotent, symmetric, and order-preserving operations on chains
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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 >]
30-May-2018
No
[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 ; Professionals ; Students
http://hdl.handle.net/10993/35930
https://arxiv.org/pdf/1805.11936.pdf

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