Brace–Daykin type inequalities for intersecting families

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Abstract

Let n,k and r8 be positive integers. Suppose that a family [n]k satisfies F1Fr for all F1,,Fr and FF=. We prove that there exist ϵr>0 and nr such that ||(r+1)nr1kr+nr1kr1 holds for all n and k, satisfying n>nr and |kn12|<ϵr.

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