Simultaneous systems of representatives for families of finite sets
Abstract: Let and . Then there exists a real number such that, if and are families of nonempty, pairwise disjoint sets with and and for all and , then , where is the number of sets such that is a minimal system of representatives for and is simultaneously a system of representatives for . A conjecture about the best possible value of the constant is proved in the case . The necessity of the disjointness conditions for the families and is also demonstrated.
-  Paul Erdős and Melvyn B. Nathanson, Systems of distinct representatives and minimal bases in additive number theory, Number theory, Carbondale 1979 (Proc. Southern Illinois Conf., Southern Illinois Univ., Carbondale, Ill., 1979) Lecture Notes in Math., vol. 751, Springer, Berlin, 1979, pp. 89–107. MR 564925
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05A05
Retrieve articles in all journals with MSC: 05A05