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Some Inequalities Concerning Cross-Intersecting Families

Published online by Cambridge University Press:  01 September 1998

P. FRANKL
Affiliation:
CNRS, ER 175 Combinatoire, 54 Bd Raspail, 75006 Paris, France (e-mail: combinatorics@cs.meiji.ac.jp)
N. TOKUSHIGE
Affiliation:
College of Education, Ryukyu University, Nishihara, Okinawa, 903–0213 Japan (e-mail: hide@edu.u-ryukyu.ac.jp)

Abstract

Let a, b and n be integers with 2[les ]a[les ]b and n[ges ]a+b. Suppose that [Ascr ]⊂([n]a) and [Bscr ]⊂([n]b) are nontrivial cross-intersecting families. Then [mid ][Ascr ][mid ]+[mid ][Bscr ][mid ][les ]2+(nb) −2(n−ab)+ (n−2ab). This result is best possible.

Type
Research Article
Copyright
1998 Cambridge University Press

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