Notes on the ordered set A^A. Part IV. The dual ^A A of A^A for finite ordered sets

2025/09/25 by George Grätzer, Grätzer, G.
Computer Science · Mathematics · #06 #Computational Geometry and Mesh Generation #FOS: Mathematics #Functional Equations Stability Results #Mathematics and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2509.20726

openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a finite ordered set. Define the ordered set A^A as the set of all maps from A to A, ordered pointwise. Let ^A A be the dual of A^A. We prove results in the spirit of Parts~I--III, but now using both A^A and ^AA. For example, if (^^ ^ ^AAAAA)^A^A^A is isomorphic to (^ ^ ^ ^BBBBB)^B^B^B for finite ordered sets A and B, then A is isomorphic to B.

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