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Results tagged with posets
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user 19729
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 $x \leq z$).
10
votes
What is the Möbius function for the lattice of partial partitions?
Hersh, Hanlon, and Shareshian characterize the Möbius function of this lattice in a never-published preprint:
A $\operatorname{GL}_n(q)$ analogue of the partition lattice.
It is often 0, but/and agree …
- 3,407
0
votes
When does a graph underlie the Hasse diagram of a poset?
I think at one point he also had some course notes posted on it; it's also in his book on dimension theory of posets. See also this post on CSTheory stackexchange. …
- 3,407
5
votes
Is an Eulerian lattice shellable?
I think that the answer to your question ought to be "not always".
There are examples of non-shellable balls and spheres. A very readable account of these, together with some of the history, can b …
- 3,407