Systems of Distinct Representatives

Authors

Dr. Evan Wantland, Department of Mathematical Sciences, University of Montana, Missoula and UM - Western Montana College

Document Type

Presentation Abstract

Presentation Date

4-19-2001

Abstract

In his famous paper of 1935, Phillip Hall answered the following question:

What are necessary and sufficient conditions on a collection of finite sets S1, S2, . . . , Sn such that there exists an n-tuple (x1, x2, . . . , xn) of n distinct elements such that xi is in Si?

We call such an n-tuple a system of distinct representatives. Since this result, there have been many related results, applications and generalizations of Hall’s Theorem.

In this presentation we will state a more general question to that above and consider how Hall’s Theorem may apply. We will discuss how previous work may be viewed through this generalization and present a few applications of this theory to universal algebra and graph coloring problems.

Additional Details

Thursday, 19 April 2001
4:10 p.m. in Math 109
Coffee/treats at 3:30 p.m. Math 104 (Lounge)

Recommended Citation

Wantland, Dr. Evan, "Systems of Distinct Representatives" (2001). Colloquia of the Department of Mathematical Sciences. 92.
https://scholarworks.umt.edu/mathcolloquia/92