A note on the ordered set $A^A$

Published 29 Aug 2025 in math.RA | (2509.00209v1)

Abstract: Let $A$ and $B$ be finite partially ordered sets (ordered sets). We show that if the ordered sets of self-maps $A^A$ and $B^B$ (ordered pointwise) are isomorphic, then $A$ and $B$ are isomorphic. This resolves a question originating with Duffus (1978), with related results by Duffus--Wille and Farley.

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G. Grätzer

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