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Rental Harmony: Sperner's Lemma in Fair Division

by Francis Su

Award: Merten Hasse

Year of Award: 2001

Publication Information: The American Mathematical Monthly, Vol. 106, No. 10, December 1999, pp. 930-942.

Summary: A powerful approach to fair-division questions that provides new methods for achieving approximate envy-free divisions, in which each person feels he or she has received the “best” share.

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About the Author: Francis Su earned his Ph.D. from Harvard in 1995 studying random walks, but his interest in fair division was a result of thesis procrastination. His research is now (fairly? randomly?) divided between studies of random walk convergence and fair division algorithms. He is an assistant professor at Harvey Mudd College, a “blue dot” MAA Project NExT Fellow, and an amateur songwriter in his spare time. Since the writing of this article he and HMC undergraduate Elisha Peterson wrote a web applet that uses an improved trapdoor algorithm; their Fair Division Calculator works for cakes, chores, or rent and they invite you to try it out at


Subject classification(s): Mathematics for Social Sciences | Discrete Mathematics
Publication Date: 
Monday, July 28, 2008