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Results tagged with posets
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user 461
A poset or partially ordered set is a set endowed with a partial order, meaning a binary relation $\leq$ which is reflexive ($x \leq x$ for all $x$), antisymmetric ($x\leq y$ and $y\leq x$ implies $x=y$), and transitive ($x\leq y$ and $y\leq z$ implies $x \leq z$).
5
votes
Posets isomorphic to their endomorphism poset
The answer to
Is there a poset with more than 1 point such that $P\cong\text{End}(P)$?
is No. This follows immediately from Theorem 3 in
Roy O. Davies, Allan Hayes and George Rousseau, Comp …
- 4,416
11
votes
0
answers
280
views
Does every finite poset have a rigid endomorphism?
Crossposted on Mathematics.
In this post, an order-preserving self-map of a poset $X$ will be called an endomorphism of $X$, and such an endomorphism $f$ will be called rigid if the only automorphism …
- 4,416