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

2018/05/30 by Jimmy Devillet, Devillet, Jimmy, Bruno Teheux +1
Computer Science · Materials Science · #05A15 #06A12 #Advanced Algebra and Logic #FOS: Mathematics #Nanocluster Synthesis and Applications #Polyoxometalates: Synthesis and Applications #Primary 20M14 #Rings and Algebras (math.RA) #Secondary 39B52

paper · pdf · doi:10.48550/arxiv.1805.11936

openalex publication_date 2018/05/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We characterize the associative, idempotent, symmetric, and order-preserving\noperations on (finite) chains in terms of properties of (the Hasse diagram of)\ntheir associated semilattice order. In particular, we prove that the number of\nassociative, idempotent, symmetric, and order-preserving operations on an\nn-element chain is the n^\th Catalan number.\n

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