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Uniform Intersecting Families with Covering Number Restrictions

Published online by Cambridge University Press:  01 March 1998

P. FRANKL
Affiliation:
CNRS, ER 175 Combinatoire, 54 Bd Raspail, 75006 Paris, France
K. OTA
Affiliation:
Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223 Japan (e-mail: ohta@comb.math.keio.ac.jp)
N. TOKUSHIGE
Affiliation:
College of Education, Ryukyu University, 1 Nishihara, Okinawa, 903/01 Japan (e-mail: hide@edu.u-ryukyu.ac.jp)

Abstract

It is known that any k-uniform family with covering number t has at most ktt-covers. In this paper, we deal with intersecting families and give better upper bounds for the number of t-covers. Let pt(k) be the maximum number of t-covers in any k-uniform intersecting families with covering number t. We prove that, for a fixed t,

formula here

In the cases of t=4 and 5, we also prove that the coefficient of kt−1 in pt(k) is exactly (t2).

Type
Research Article
Copyright
1998 Cambridge University Press

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