Mathematics
DOI: 10.1112/jlms/s1-10.37.26

tlooto Summary

Researchers prove that a set R of m things can represent both classes (a) and (b) from set S with mn elements.

Abstract

Let a set S of mn things be divided into m classes of n things each in two distinct ways, (a) and (b); so that there are m (a)-classes and m (b)-classes. Then it is always possible to find a set R of m things of S which is at one and the same time a C.S.R. (= complete system of rcpresentatives) for the (a)-classes, and also a C.S.R. for the (b)-classes.

Citation format

HALL, P. On representatives of subsets. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1935: 26–30.