Geodesic
Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978
Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 435-446.

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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 $P\cong Q$.
DOI : 10.21136/MB.2022.0010-22
Classification : 06A07
Keywords: (partially) ordered set; exponentiation; connected 
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Farley, Jonathan David. Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978. Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 435-446. doi : 10.21136/MB.2022.0010-22. http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0010-22/

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