Research Papers and Preprints

You can probably tell that my research interests have varied quite a bit. My Ph.D. was a mix of representation theory and probability used to analyze random walks on algebraic structures. More recently, I’ve been fascinated by mathematical questions arising from problems in the social sciences. I’ve been carving out a niche solving problems in geometric and topological combinatorics (e.g., triangulations of polytopes and fixed point theorems) and using them to study problems of fair division in mathematical economics, and voting problems in game theory.

Be aware that preprints below may differ slightly from the published versions. Many of my papers have been jointly authored with undergraduates. Cell colors group related papers.

* = undergraduate co-authors

1. Francis Edward Su. Methods for Quantifying Rates of Convergence for Random Walks on Groups. 
Ph.D. Thesis, Harvard University. Advisor: Persi Diaconis.

2. Francis Edward Su. Borsuk-Ulam implies Brouwer: a direct construction.
Amer. Math. Monthly, 104(9):855–859, 1997.

3. Francis Edward Su. Convergence of random walks on the circle generated by an irrational rotation.
Trans. Amer. Math. Soc., 350(9):3717–3741, 1998.

4. Francis Edward Su. Rental harmony: Sperner’s lemma in fair division. 
Amer. Math. Monthly, 106(10):930–942, 1999.
[PDF] This article was awarded the MAA’s 2001 Merten M. Hasse Prize for mathematical exposition.

5. Arthur T. Benjamin, Jennifer J. Quinn, and Francis Edward Su. Phased tilings and generalized Fibonacci identities. 
Fibonacci Quart., 38(3):282–288, 2000.

6. Arthur T. Benjamin, Francis Edward Su, and Jennifer J. Quinn. Counting on Continued Fractions. 
Math. Mag., 73(2):98–104, 2000. 

7. Francis Edward Su. A LeVeque-type lower bound for discrepancy. 
In Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA), pages 448–458. Springer, Berlin, 2000. 

8. Francis Edward Su. Reviews: Cake-Cutting Algorithms: Be Fair if You Can. 
Amer. Math. Monthly, 107(2):185–188, 2000.

9. Matthias G. Raith, and Francis Edward Su. Procedural support for cooperative negotiations: theory and implementation. 
In Advances in Decision Technology and Intelligent Information Systems, Volume I, pages 21–36. The International Institute for Advanced Studies in Systems Research and Cybernetics, Windsor, Canada, 2000.

10. Francis Edward Su. Discrepancy convergence for the drunkard’s walk on the sphere. 
Electron. J. Probab., 6:no. 2, 20 pp. (electronic), 2001.

11. Jesus A. De Loera, Elisha Peterson*, and Francis Edward Su. A polytopal generalization of Sperner’s lemma. 
J. Combin. Theory Ser. A, 100(1):1–26, 2002.
[PDF]12. Claus-Jochen Haake, Matthias G. Raith, and Francis Edward Su. Bidding for envy-freeness: a procedural approach to n-player fair-division problems. 
Soc. Choice Welf., 19(4):723–749, 2002.
[PDF] This algorithm in this paper has been implemented in The Fair Division Calculator (New York Times Version).

13. Elisha Peterson* and Francis Edward Su. Four-Person Envy-Free Chore Division.
Math. Mag., 75(2):117–122, 2002.

14. Alison L. Gibbs and Francis Edward Su. On choosing and bounding probability metrics.
International Statistical Review, 70(3):419–435, 2002.
[PDF] Version February 2002.

15. Arthur T. Benjamin, Christopher R. H. Hanusa*, and Francis Edward Su. Linear recurrences through tilings and Markov chains. 
Util. Math., 64:3–17, 2003.
[PDF] Version June 2001.

16. Forest W. Simmons and Francis Edward Su. Consensus-halving via theorems of Borsuk-Ulam and Tucker. 
Math. Social Sci., 45(1):15–25, 2003. 

17. Doug Hensley and Francis Edward Su. Random walks with badly approximable numbers. 
In Unusual applications of number theory, volume 64 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci., pages 95–101. Amer. Math. Soc., Providence, RI, 2004.

18. Timothy Prescott* and Francis Edward Su. Random walks on the torus with several generators. 
Random Structures Algorithms, 25(3):336–345, 2004.
[PDF at the arXiv] Version April 2004.

19. Adam Bliss* and Francis Edward Su. Lower bounds for simplicial covers and triangulations of cubes. 
Discrete Comput. Geom., 33(4):669–686, 2005.
[PDF at the arXiv]

20. Timothy Prescott* and Francis Edward Su. A constructive proof of Ky Fan’s generalization of Tucker’s lemma. 
J. Combin. Theory Ser. A, 111(2):257–265, 2005.
[PDF at the arXiv]

21. Douglas Rizzolo* and Francis Edward Su. A fixed point theorem for the infinite-dimensional simplex. 
J. Math. Anal. Appl., 332(2):1063–1070, 2007.
[PDF at the arXiv]

22. Gwen Spencer* and Francis Edward Su. The LSB theorem implies the KKM lemma. 
Amer. Math. Monthly, 114(2):156–159, 2007.
[PDF at the arXiv]

23. Claus-Jochen Haake, Akemi Kashiwada*, and Francis Edward Su. The Shapley value of phylogenetic trees. 
J. Math. Biol., 56(4):479–497, 2008.
[PDF at the arXiv]

24. Deborah Berg*, Serguei Norine, Francis Edward Su, Robin Thomas, and Paul Wollan. Voting in agreeable societies. 
Amer. Math. Monthly 117:27–39, 2010.
[PDF at the arXiv]

25. John Cloutier*, Kathryn L. Nyman, and Francis Edward Su. Two-player envy-free multi-cake division. 
Math. Social Sci. 59:26–37, 2010. 
[PDF at the arXiv]

26. Francis Edward Su. Teaching Research: Encouraging Discoveries.  Amer. Math. Monthly, 117:159–169, 2010.
Reprinted in Best Writing on Mathematics 2011 (M. Pitici, ed.), Princeton University Press, 2011.

27. Francis Edward Su. The agreeable society theorem. 
In Expeditions in Mathematics (Shubin, Hayes, Alexanderson, eds.), Mathematical Association of America, 2011.
[PDF at the arXiv]

28. Sanjai Gupta, Parousia Rockstroh*, and Francis Edward Su. Splitting fields and periods of Fibonacci sequences modulo primes. 
Math. Mag., Volume 85, Number 2, April 2012, 130-135. 
[PDF at the arXiv]

Not Yet Published

29. Rosalie Carlson*, Stephen Flood, Kevin O’Neill*, and Francis Edward Su. A Turan-type theorem for circular arc graphs. 
[PDF at the arXiv]

30. Claus-Jochen Haake and Francis Edward Su. Fair division procedures: why use Mathematics? 
In Procedural Approaches to Conflict Resolution (Matthias Raith, ed.), to appear.

31. Zeph Landau and Francis Edward Su. Fair division and redistricting. 

32. Elisha Peterson* and Francis Edward Su. N-person envy-free chore division.
[PDF at the arXiv]

33. Kyle E. Kinneberg*, Aaron Mazel-Gee*, Tia Sondjaja*, and Francis Edward Su. A cubical antipodal theorem.
[PDF at the arXiv]

34. Andrew Niedermaier*, Douglas Rizzolo* and Francis Edward Su. Sperner and KKM-type theorems on trees and cycles.
[PDF at the arXiv]

35. Tyler Seacrest* and Francis Edward Su. Minimal triangulations of simplotopes.
[PDF at the arXiv]

36. Sarah Fletcher*, Christopher Hardin, and Francis Edward Su. The agreement number of tree societies.

Other Writings

The Banach-Tarski Paradox.  An expository paper for my Minor Thesis requirement, Harvard University.