Laszlo Zadori - Finite posets with symmetric idempotent operations

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Laszlo Zadori - Finite posets with symmetric idempotent operations

LASZLO ZADORI, U. Szeged

Finite posets with symmetric idempotent operations

An n-ary operation f is totally symmetric if it obeys the identity $f(x_1,\dots,x_n)=f(y_1,\dots,y_n)$ for all sets of variables such that $\{x_1,\dots,x_n\}=\{y_1,\dots,y_n\}$ . A characterization of finite posets admitting an n-ary idempotent totally symmetric operation for all n is given. The characterization is expressed in terms of zigzags, special objects assigned to the poset. Related problems concerning idempotent Malcev conditions for order primal algebras are mentioned in the talk.