Abstract
We seek families of subsets of an n-set of given size that contain the fewest k-chains.
We prove a “supersaturation-type” extension of both Sperner’s Theorem (1928) and
its generalization by Erd˝os (1945). Erd˝os showed that a largest k-chain free family
in the Boolean lattice is formed by taking all subsets of the (k
We prove a “supersaturation-type” extension of both Sperner’s Theorem (1928) and
its generalization by Erd˝os (1945). Erd˝os showed that a largest k-chain free family
in the Boolean lattice is formed by taking all subsets of the (k
| Original language | English |
|---|---|
| Article number | A4 |
| Pages (from-to) | 1-7 |
| Number of pages | 7 |
| Journal | Integers : electronic journal of combinatorial number theory |
| Volume | 14A |
| Publication status | Published - 14 May 2014 |