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Results tagged with lattice-theory
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user 136218
The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
4
votes
1
answer
155
views
Remove an edge from the Hasse diagram of a finite lattice
If we remove an edge from the Hasse diagram of a finite lattice, as long as any vertex maintain at least one upward edge and at least one downward edge, do we still always have a lattice from the resu …
- 990
0
votes
1
answer
225
views
Minimum number of elements needed to represent a lattice with a union-closed family of sets
I know that it is possible to represent every finite lattice $L$ with a union-closed family $\mathcal{F}$ containing the empty set: for every $x\in L$, let $S_x=\{y\in L\, :\, y\not\geq x\}$ and $\ma …
- 990
0
votes
Accepted
Minimum number of elements needed to represent a lattice with a union-closed family of sets
Let $\mathcal{F} = \{S_x :\, x\in L\}$ and $S_x=\{y\in L\, :\, y\not\geq x,\, y \not= a \land b\}$, i.e. $y$ must be meet-irreducible, for the following lattice $L$:
where the meet-irreducible elemen …
- 990
5
votes
0
answers
129
views
Looking for a certain finite lattice
I don't think it actually exists, and it should be difficult proving that it doesn't (some background here), but is it possible to build a finite lattice $L$ where the only meet-irreducible elements a …
- 990