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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

Enumerating Optimal Solutions to Special Instances of the Lottery Problem

AP Burger1, JH van Vuuren1
1Department of Logistics, University of Stellenbosch, Private Bag X1, Matieland, 7602, South Africa
  • Published: 30/11/2007

Abstract

In this paper, we determine analytically the number of balanced, unlabelled, 3-member covers of an unlabelled finite set, which is then used to find the number of non-isomorphic optimal lottery sets of cardinality three. We also determine numerically the number of non-isomorphic optimal playing sets for lotteries in which a single correct number is required to win a prize.

Keywords: Lottery set, (unlabelled) set cover, enumeration. AMS Classification: 05B05, 05B40, 05C69, 62K05, 62K10.
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Citation
AP Burger, JH van Vuuren. Enumerating Optimal Solutions to Special Instances of the Lottery Problem[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 063. 47-63. DOI: .