article

Some special vapnik-chervonenkis classes

Authors:

R. S. Wenocur,

R. M. DudleyAuthors Info & Claims

Discrete Mathematics, Volume 33, Issue 3

Pages 313 - 318

https://doi.org/10.1016/0012-365X(81)90274-0

Published: 01 January 1981 Publication History

Abstract

For a class C of subsets of a set X, let V(C) be the smallest n such that no n-element set F@__ __X has all its subsets of the form A @__ __ F, A @__ __ C. The condition V(C) <+~ has probabilistic implications. If any two-element subset A of X satisfies both A @__ __ C = O and A @__ __ D for some C, D@__ __C, then V(C)=2 if and only if C is linearly ordered by inclusion. If C is of the form C={@__ __^n"i"="1 C"i:C"i@__ __C"i, i=1,2,...,n}, where each C"i is linearly ordered by inclusion, then V(C)= 0} for f in H, then V(C)=n.

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Discrete Mathematics Volume 33, Issue 3

January, 1981

97 pages

ISSN:0012-365X

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 January 1981

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