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See detailAssociative, idempotent, symmetric, and order-preserving operations on chains
Devillet, Jimmy UL; Teheux, Bruno UL

in Order: A Journal on the Theory of Ordered Sets and its Applications (2020), 37(1), 45-58

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 ... [more ▼]

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. [less ▲]

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