• Corpus ID: 235391058

Best possible bounds on the number of distinct differences in intersecting families

  title={Best possible bounds on the number of distinct differences in intersecting families},
  author={Peter Frankl and S. G. Kiselev and Andrey B. Kupavskii},
For a family F , let D(F) stand for the family of all sets that can be expressed as F ∖ G, where F,G ∈ F . A family F is intersecting if any two sets from the family have non-empty intersection. In this paper, we study the following question: what is the maximum of |D(F)| for an intersecting family of k-element sets? Frankl conjectured that the maximum is attained when F is the family of all sets containing a fixed element. We show that this holds if n > 50k log k and k > 50. At the same time… 
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  • P. Frankl
  • Mathematics
    J. Comb. Theory, Ser. A
  • 1987
2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set
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R. L. Graham has posed the following question: Given n positive integers a1, < a2 <… < an, does there exists a pair of indices i, j such that ai/(ai, aj) ⩾ n? ((ai, aj) = g.c.d. of ai and aj).
Combinatorial problems and exercises
Problems Hints Solutions Dictionary of the combinatorial phrases and concepts used Notation Index of the abbreviations of textbooks and monographs Subject index Author index Errata.
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  • 1963