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Sperner systems consisting of pairs of complementary subsets

✍ Scribed by Béla Bollobás

Book ID
107884771
Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
163 KB
Volume
15
Category
Article
ISSN
0097-3165

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Let X be an n-element set and 2' be the family of subsets of X. If&C c 2' such that for any K. K\_ F .%'" K. f K\_ it-dim K. ct K. then Wr is ca!!pd a Sn~rtwr wstem Let \_M be 8~ ,+\_ x g \_\_l'\_\_L-~" '\_\_I , \_\_' \_\_\_\_=\_\_ \_\_ \_\_I i \_\_' \_ .

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✍ G. Greco 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 119 KB

A family F of subsets of a finite set X shatters a set D X, if the intersections of the members of F with D coincide with the power set of D. The maximum size of a set shattered by F is the VC-dimension (or density) of the system. P. Frankl (1983, J. Combin. Theory Ser. A 34, 41 45) investigates the