Enumerating Optimal Solutions to Special Instances of the Lottery Problem

Alewyn P Burger¹ & Jan H van Vuuren²

Abstract

In this paper a 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.

An electronic version of the complete paper may be obtained here: [ps] [pdf].

Affiliations

¹ Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa, email: apburger@sun.ac.za. ² Department of Applied Mathematics, Stellenbosch University, Private Bag X1, Matieland, 7602, Republic of South Africa, email: vuuren@sun.ac.za.

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