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Results tagged with posets
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user 468
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
Accepted
Extending subsets to supersets in different ways
The answer is no. Here is a list of sets $A_i$ and $B_i$ which fails.
12, 1234
23, 1235
13, 1236
14, 1245
25, 2356
36, 1346
45, 1456
56, 2456
46, 3456
The failure can be seen by drawing the pictu …
- 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