On the lottery problem

✍ Scribed by Zoltán Füredi; Gábor J. Székely; Zoltán Zubor

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 290 KB
• Volume: 4
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/(sici)1520-6610(1996)4:1<5::aid-jcd2>3.0.co;2-j

✦ Synopsis

Let L(n,

k,

k,

t

) denote the minimum number of k-subsets of an n-set such that all the ( i ) k-sets are intersected by one of them in at least t elements. In this article L(n,k,k,Z) is calculated for infinite sets of n's. We obtain L(90,5,5,2) = 100, i.e., 100 tickets needed to guarantee 2 correct matches in the Hungarian Lottery. The main tool of proofs is a version of Turan's theorem due to Erd6s. 0 1996 John Wiley & Sons, Inc.

1 . STEINER SYSTEMS AND &COVERS

A system of k-element subsets, C , of an n-element underlying set V is called an (n, k, t)cover if every t-subset T C V is contained in some member of it, T C C E C. The minimum size of an ( n , k, t)-cover is denoted by C ( n , k, t ) . A k-set covers exactly ( f )