Brace-Daykin type inequalities for intersecting families

Abstract

Let n,k and r ≥ 8 be positive integers. Suppose that a family F ⊂ ([n] k ) satisfies F1∩·· ·∩Fr 6= / 0 for all F1, . . . ,Fr ∈F and ⋂ F∈F F = / 0. We prove that there exist εr > 0 and nr such that |F | ≤ (r +1) ( n− r−1 k− r ) + ( n− r−1 k− r−1 ) holds for all n and k, satisfying n > nr and | k n − 2 |< εr. 
DOI: 10.1016/j.ejc.2006.09.001

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