Some notes on the combinatorial properties of haplotype tagging

Tagging haplotypes with a small number of genetic markers is becoming an increasingly interesting and important problem. Surprisingly little work has been done to characterize the mathematical framework of this problem. In this paper we present a mathematical frame, based on Boolean algebras, that adequately describe the structure of a set of genetic bi-allelic markers and the corresponding set of haplotypes. We derive a number of results that relate the number of markers required to tag a set of haplotypes to the set of markers themselves.