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Winning the lottery. (English) Zbl 0864.05008

Colbourn, Charles J. (ed.) et al., The CRC handbook of combinatorial designs. Boca Raton, FL: CRC Press. CRC Press Series on Discrete Mathematics and its Applications. 578-584 (1996).
A summary is given of how to purchase a minimum number of lottery tickets in order to be sure of matching at least \(t\) of the numbers in the lottery. A lottery scheme is a collection of lottery tickets that ensure this happens. The question then is to determine the minimal number of tickets needed for a lottery scheme. Lower bound estimates are given for this number based on Turán designs and \(t\)-\((n,k,1)\) coverings. Furthermore, examples are given which give an upper bound for some cases.
For the entire collection see [Zbl 0836.00010].
Reviewer: N.Brand (Denton)

MSC:

05A99 Enumerative combinatorics
05B30 Other designs, configurations