Uniform Intersecting Families with Covering Number Restrictions

P. Frankl, K. Ota, N. Tokushige

研究成果: Article査読

2 被引用数 (Scopus)

抄録

It is known that any k-uniform family with covering number t has at most kt t-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, pt(k) ≤ kt - 1/√2 ⌊t-1/2⌋3/2kt-1 + O(kt-2). In the cases of t = 4 and 5, we also prove that the coefficient of kt-1 in pt(k) is exactly (t2).

本文言語English
ページ(範囲)47-56
ページ数10
ジャーナルCombinatorics Probability and Computing
7
1
DOI
出版ステータスPublished - 1998

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 統計学および確率
  • 計算理論と計算数学
  • 応用数学

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