A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf
.
Simultaneous Systems of Representatives for Families of Finite Sets
1988
Proceedings of the American Mathematical Society
Let h > 2 and k > 1. Then there exists a real number A = \(h,k) e (0,1) such that, if S" = {Si}si=1 and 3~ = {3>}i_, are families of nonempty, pairwise disjoint sets with |S¿| < h and |Tj-| < k and S¿ C¿ Tj for all i and j, then N(5^,^) < /i3A(, where N(5^,J') is the number of sets X such that X is a minimal system of representatives for 5? and X is simultaneously a system of representatives for !?. A conjecture about the best possible value of the constant \(h, k) is proved in the case h > k.
doi:10.2307/2047133
fatcat:wgwvcltvwbhalicw65vzqlu6m4