Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978
Duffus wrote in his 1978 Ph.D. thesis, "It is not obvious that $P$ is connected and $P^P\cong Q^Q$ imply that $Q$ is connected", where $P$ and $Q$ are finite nonempty posets. We show that, indeed, under these hypotheses $Q$ is connected and $P\cong Q$.
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2023-12-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/148/4/mb148_4_1.pdf |