Minimum number of subsets to distinguish individual elements
Philip R. Meyers · Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics · 1967
Given a set S of card in al ity tn , we determine the minimum cardinality/(m) for a family F of s ub sets of S s uch that each SES can be expressed as the intersection of some subfamily of F. Th e problem is solv ed in the following inverse form.For a given numbe r II of subsets of S, find g(Il): the maximum number of elements of S which can be written as the intersec tion of so m e of th ese s ubsets.We s how that g(ll) is the largest binomial coefficient for com binations of II things.