Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T05:01:49.845Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Inequalities Concerning Cross-Intersecting Families

Published online by Cambridge University Press:  01 September 1998

P. FRANKL  and
N. TOKUSHIGE
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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 3 , September 1998 , pp. 247 - 260
Copyright
1998 Cambridge University Press