Hall's Marriage Theorem

An algebraic approach to Halls matching theorem

The purpose of this note is to present a proof of Hall's matching theorem (also called marriage theorem) which I have not encountered elsewhere in literature-what yet does not mean that it is necessarily new. We refer to Hall's theorem in the following form: Theorem 1 (Hall). Let n be a positive integer. Let be a bipartite graph whose set of vertices consists of n blue vertices B 1 ; B 2 Some n...

Religious Assortative Marriage in the Netherlands , 1938 - 1983

An algebraic approach to Halls matching theorem abridged version

The purpose of this note is to present a proof of Hall's matching theorem (also called marriage theorem) which I have not encountered elsewhere in literature-what yet does not mean that it is necessarily new. We refer to Hall's theorem in the following form: Theorem 1 (Hall). Let n be a positive integer. Let be a bipartite graph whose set of vertices consists of n blue vertices B 1 ; B 2 Some n...

Two classes of q-ary codes based on group divisible association schemes

By means of Hall's Marriage Theorem, a class of q-ary codes are obtained through block designs based on group divisible association schemes with two associate classes. If these block designs are further semiframes, another class of q-ary codes are also constructed. @ 1999 Elsevier Science B.V. All rights reserved

Proof-Theoretic Strength of the Stable Marriage Theorem and Other Problems

We study the proof theoretic strength of several infinite versions of finite combinatorial theorem with respect to the standard Reverse Mathematics hierarchy of systems of second order arithmetic. In particular, we study three infinite extensions of the stable marriage theorem of Gale and Shapley. Other theorems studied include some results on partially ordered sets due to Dilworth and to Dushn...