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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.00209 |
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| _version_ | 1866914069029584896 |
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| author | Grätzer, G. |
| author_facet | Grätzer, G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on the ordered set $A^A$. Part I. The classical problem Grätzer, G. Rings and Algebras 06 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. |
| title | Notes on the ordered set $A^A$. Part I. The classical problem |
| topic | Rings and Algebras 06 |
| url | https://arxiv.org/abs/2509.00209 |