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On the lottery problem
Author(s) -
Füredi Zoltán,
Székely Gábor J.,
Zubor Zoltán
Publication year - 1996
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1996)4:1<5::aid-jcd2>3.0.co;2-j
Subject(s) - lottery , mathematics , combinatorics , mathematical proof , set (abstract data type) , discrete mathematics , statistics , computer science , geometry , programming language
Let L(n,k,k,t) denote the minimum number of k ‐subsets of an n ‐set such that all the ( n k ) k ‐sets are intersected by one of them in at least t elements. In this article L(n,k,k,2) 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 Turán's theorem due to Erdös. © 1996 John Wiley & Sons, Inc.