Ranking functions and axioms for linear orders
The problem of ranking n competitors by their results after participation in r races is studied. For fixed n and r there exist the set of all results denoted \(L(n,r)\). \(L(n,r)\) is considered a distributive lattice with the partial order P on it. The isomorphism between \(L(p,q)\) and \(L(q+1,p-1)\) is shown. The notion of dimension of this set is considered. Two axioms are given for the set of results and the notion of dimension is investigated for linear orders with respect to these axioms. For the particular case \((n=0\), \(r\geq 2)\) it is proved that \(L(3,r)\) has dimension \(D(n,r)=2\). A more common theorem is proved by \textit{W. T. Trotter} and \textit{V. Rödl} [reviewed below (see Zbl 0646.06004)].
scientific article; zbMATH DE number 4053691
scientific article