We prove the following theorem concerning the poset of all subsets of [n] ordered by inclusion. Consider any two equal-size families of subsets of [n], S and R, where within each family all subsets have the same number of elements. Suppose there exists a bijection ,: S [ R such that A#f (A) for all
A Sperner theorem on unrelated chains of subsets
✍ Scribed by Jerrold R Griggs; Jürgen Stahl; William T Trotter Jr.
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 169 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0097-3165
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📜 SIMILAR VOLUMES
One of the best-known results of extremal combinatorics is Sperner's theorem, which asserts that the maximum size of an antichain of subsets of an n-element set equals the binomial coefficient n n/2 , that is, the maximum of the binomial coefficients. In the last twenty years, Sperner's theorem has
A subset A of a poset P is a q-anti&in if it can be obtained as the union of at most q antichains. A ranked poset P is said to be q-Sperner if the maximum number of elements of a q-antichain of P is the sum of the cardinalities of its q larger rank-sets. P is strongly Spernu if it is q-Sperner for a