Forbidden (0,1)-vectors in hyperplanes of R-n: The restricted case
In this paper we continue our investigation on "Extremal problems under dimension constraint" introduced in [2]. Let E(n, k) be the set of (0,1)-vectors in R-n with k one's. Given 1 less than or equal to m, w less than or equal to n let X subset of E(n, m) satisfy span(X) boolean AND E(n, w) = empty set. How big can \X\ be? This is the main problem studied in this paper. We solve this problem for all parameters 1 less than or equal to m, w less than or equal to n and n > n(0) (m, w).
(0,1)-vectors dimension constraint combinatorial extremal theory forbidden weights nontrivial intersecting systems