Notes on the ordered set A^A. Part I. The classical problem

2025/08/29 by G. Grätzer, Grätzer, G.
Computer Science · Mathematics · #06 #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2509.00209

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A and B be finite ordered sets. We show that if the ordered sets of isotone self-maps A^A and B^B (ordered pointwise) are isomorphic, then A and B are isomorphic. This resolves a question originating with D. Duffus in 1978, with related results by D. Duffus--R. Wille in 1979 and J. Farley in 2023.

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