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Results tagged with posets
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user 123731
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 $x \leq z$).
4
votes
1
answer
170
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(Higher) posets with non-binary comparisons: name? Axioms? (Looking for reference.)
I am looking for a name of a certain structure, which is a generalization of poset that admits non-binary comparisons.
Let $P$ be a set equipped with operations, for $n\geq2$,
$$ C_n: P^n \to \{True, …
- 765
3
votes
1
answer
102
views
What property of ranked poset ensures that it is determined by its vertex-facet incidences?
For a convex polytope, its face poset is combinatorially determined by vertex-facet incidences. Now suppose we have an arbitrary finite poset that is ranked, so I can still speak of vertices and facet …
- 765
3
votes
0
answers
111
views
"Slim" directed polytopes: any established name for them?
This is a "looking for context" question.
Let's say that a polytope is directed if its 1-skeleton is an oriented graph with no cycles, one source, one sink. (Edit: let us additionally assume that ever …
- 765