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Results tagged with lattice-theory
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user 468
The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
6
votes
How is the free modular lattice on 3 generators related to 8-dimensional space?
Edited to be more of an answer. But, unfortunately, to be quite wrong. I apologize for having been borne away by my enthusiasm.
The picture of the free modular lattice above shows thirty elements. …
- 6,302
4
votes
Accepted
Finite lattices whose number of join-irreducibles does not exceed its height
Join semi-distributive lattices don't have this property because weak order on $S_n$ is join semi-distributive and doesn't have this property. (Eg, for $n=3$.)
Lattices satisfying the property you a …
- 6,302
4
votes
Accepted
Enumerative characterisation of boolean lattices
Define a ground set $X$ of size $2^{n-1}$. Now choose $2^{n-1}-(n-1)$ subsets of $X$, each of size at least 2, such that the sum of their sizes is $(n-2)2^{n-1}+2$ (so the average size is slightly mo …
- 6,302