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Does the endomorphism poset $P^{P}$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978

Jonathan David Farley — 2023

Mathematica Bohemica

Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that $P$ is connected and $P^{P} ≅ Q^{Q}$ imply that $Q$ is connected”, where $P$ and $Q$ are finite nonempty posets. We show that, indeed, under these hypotheses $Q$ is connected and $P ≅ Q$ .

Chain polynomials of distributive lattices are 75% unimodal.

Björner, Anders; Farley, Jonathan David — 2005

The Electronic Journal of Combinatorics [electronic only]

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Does the endomorphism poset P P determine whether a finite poset P is connected? An issue Duffus raised in 1978

Chain polynomials of distributive lattices are 75% unimodal.

Does the endomorphism poset $P^{P}$ determine whether a finite poset $P$ is connected? An issue Duffus raised in 1978