Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-25T01:04:29.022Z 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)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)