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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 $x \leq z$).
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Not sure whether I find a counterexample to poset fiber theorem
But when I implement the theorem to the following example, the result seems inconsistent with my knowledge:
The posets are as shown in their Hasse diagrams and how the map is defined is: fixing $3,6,9,10 …
5
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Accepted
Not sure whether I find a counterexample to poset fiber theorem
I corrected my computation and it turns out the assumptions required by Theorem 1.1 in the paper are not satisfied. Many thanks to everyone, who spent time reading my long writing. Cheers.