{"id":215,"date":"2019-06-13T04:20:57","date_gmt":"2019-06-13T04:20:57","guid":{"rendered":"http:\/\/francis-su.104.42.120.246.xip.io\/?page_id=215"},"modified":"2025-04-02T23:51:44","modified_gmt":"2025-04-02T23:51:44","slug":"research-papers-and-preprints","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/su\/research-papers-and-preprints\/","title":{"rendered":"Research"},"content":{"rendered":"\n

You can probably tell that my research interests have changed over the years. 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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

If my recent papers are not here yet, they may appear on my CV<\/a> or on the arXiV<\/a>. Some older papers are available through links at Google Scholar<\/a>.<\/p>\n\n\n\n

* = undergraduate co-authors<\/p>\n\n\n\n

40. R. Alvarado, M. Averett, B. Gaines, C. Jackson, M. L. Karker, M. A. Marciniak, F. E. Su, S. Walker, The Game of Cycles.
The American Mathematical Monthly<\/em> 128 (2021), 868\u2013887.
<\/p>\n\n\n\n

39. K. Nyman, F. E. Su, S. Zerbib, Fair division with multiple pieces.
Discrete Applied Mathematics<\/em> 283 (2020), 115\u2013122.
arXiv:1710.09477<\/a><\/p>\n\n\n\n

38. F. Meunier and F. E. Su. Multilabeled versions of Sperner\u2019s and Fan\u2019s lemmas and applications.
SIAM Journal on Applied Algebra and Geometry<\/em> 3(2019), 391\u2013411.
arXiv:1801.02044<\/a> <\/p>\n\n\n\n

37. F. E. Su and S. Zerbib, Piercing Numbers in Approval Voting.
Mathematical Social Sciences<\/em> 101(2019), 65\u201371.
arXiv:1710.09493<\/a> <\/p>\n\n\n\n

36. T. Seacrest* and F. E. Su. A lower bound technique for triangulations of simplotopes.
SIAM Journal on Discrete Mathematics<\/em> 32(2018) 1\u201328.
arXiv:0910.1134<\/a> <\/p>\n\n\n\n

35. F. E. Su, Mathematics for Human Flourishing.
Amer. Math. Monthly<\/em> 124(2017), 483\u2013493.
Also in The Best Writing on Mathematics<\/em> 2018 (Mircea Petici, ed.), Princeton University Press, 2018.
Winner of the 2018 MAA Halmos-Ford Award for outstanding mathematical exposition.<\/p>\n\n\n\n

34. B. Kuture*, C. Loa*, O. Leong*, M. Sondjaja, F. E. Su, Proving Tucker\u2019s lemma with a volume argument.
Contemporary Mathematics<\/em> 685(2017), pp. 223\u2013230.
arXiv:1604.02395<\/a><\/p>\n\n\n\n

33. F. E. Su,The Lesson of Grace in Teaching. 2013 Haimo Award Lecture.
In The Best Writing onMathematics 2014<\/em> (Mircea Petici, ed.), Princeton University Press, 2014.<\/p>\n\n\n\n

32. M. Davis, M. E. Orrison, and F. E. Su. Voting for committees in agreeable societies.
Contemporary Mathematics<\/em> 624(2014), 147\u2013157.
arXiv:1402.0861<\/a><\/p>\n\n\n\n

31. M. M. Klawe, K. L. Nyman, J. N. Scott*, and F. E. Su. Double-interval societies.
Contemporary Mathematics<\/em> 624(2014), 135\u2013146.
arXiv:1307.5094<\/a> <\/p>\n\n\n\n

30. Z. Landau and F. E. Su. Fair division and redistricting.
Contemporary Mathematics<\/em> 624(2014), 17\u201336.
arXiv:1402.0862<\/a><\/p>\n\n\n\n

29. A. Niedermaier*, D. Rizzolo*, and F. E. Su. A Tree Sperner Lemma.
Contemporary Mathematics<\/em> 625(2014), 77\u201392.
arXiv:0909.0339<\/a><\/p>\n\n\n\n

28. K. Nyman and F. E. Su. A Borsuk-Ulam equivalent that implies Sperner\u2019s Lemma.
Amer. Math. Monthly<\/em> 120(2013), 346\u2013354.<\/p>\n\n\n\n

27. Sanjai Gupta, Parousia Rockstroh*, and Francis Edward Su. Splitting fields and periods of Fibonacci sequences modulo primes. 
Math. Mag.<\/em> Volume 85, Number 2, April 2012, 130-135.
arXiv:0909.0362<\/a><\/p>\n\n\n\n

26. Francis Edward Su. The agreeable society theorem. 
In Expeditions in Mathematics<\/em><\/a> (Shubin, Hayes, Alexanderson, eds.), Mathematical Association of America, 2011.
[PDF at the arXiv]<\/a><\/p>\n\n\n\n

25. Francis Edward Su. Teaching Research: Encouraging Discoveries.  Amer. Math. Monthly,<\/em> 117:159\u2013169, 2010.
[PDF]<\/a>
Reprinted in Best Writing on Mathematics 2011<\/em><\/a> (M. Pitici, ed.), Princeton University Press, 2011.<\/em><\/p>\n\n\n\n

24. Deborah Berg*, Serguei Norine, Francis Edward Su, Robin Thomas, and Paul Wollan. Voting in agreeable societies. 
Amer. Math. Monthly <\/em>117:27–39, 2010.
arXiv:0811.3245<\/a> <\/p>\n\n\n\n

23. John Cloutier*, Kathryn L. Nyman, and Francis Edward Su. Two-player envy-free multi-cake division. 
Math. Social Sci.<\/em> 59:26–37, 2010.
arXiv:0909.0301<\/a> <\/p>\n\n\n\n

22. Claus-Jochen Haake, Akemi Kashiwada*, and Francis Edward Su. The Shapley value of phylogenetic trees. 
J. Math. Biol.,<\/em> 56(4):479\u2013497, 2008.
arXiv:q-bio\/0506034<\/a>  <\/p>\n\n\n\n

21. Douglas Rizzolo* and Francis Edward Su. A fixed point theorem for the infinite-dimensional simplex. 
J. Math. Anal. Appl.,<\/em> 332(2):1063\u20131070, 2007.
arXiv:math\/0610707<\/a> <\/p>\n\n\n\n

20. Gwen Spencer* and Francis Edward Su. The LSB theorem implies the KKM lemma. 
Amer. Math. Monthly, <\/em>114(2):156\u2013159, 2007.
arXiv:math\/0409092<\/a>  <\/p>\n\n\n\n

19. Timothy Prescott* and Francis Edward Su. A constructive proof of Ky Fan’s generalization of Tucker’s lemma. 
J. Combin. Theory Ser. A,<\/em> 111(2):257\u2013265, 2005.
[PDF with errata in comments<\/a>]<\/p>\n\n\n\n

18. Adam Bliss* and Francis Edward Su. Lower bounds for simplicial covers and triangulations of cubes. 
Discrete Comput. Geom.,<\/em> 33(4):669\u2013686, 2005.
arXiv:math\/0310142<\/a> <\/p>\n\n\n\n

17. Doug Hensley and Francis Edward Su. Random walks with badly approximable numbers. 
In Unusual applications of number theory, <\/em>volume 64 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci.,<\/em> pages 95\u2013101. Amer. Math. Soc., Providence, RI, 2004.
[PDF]<\/a><\/p>\n\n\n\n

16. Timothy Prescott* and Francis Edward Su. Random walks on the torus with several generators. 
Random Structures Algorithms,<\/em> 25(3):336\u2013345, 2004.
arXiv:math\/0309011<\/a> Version April 2004.<\/p>\n\n\n\n

15. Forest W. Simmons and Francis Edward Su. Consensus-halving via theorems of Borsuk-Ulam and Tucker. 
Math. Social Sci.,<\/em> 45(1):15\u201325, 2003. 
[PDF]<\/a><\/p>\n\n\n\n

14. Arthur T. Benjamin, Christopher R. H. Hanusa*, and Francis Edward Su. Linear recurrences through tilings and Markov chains. 
Util. Math.,<\/em> 64:3\u201317, 2003.
[PDF]<\/a> Version June 2001.<\/p>\n\n\n\n

13. Jesus A. De Loera, Elisha Peterson*, and Francis Edward Su. A polytopal generalization of Sperner’s lemma. 
J. Combin. Theory Ser. A,<\/em> 100(1):1\u201326, 2002.
[PDF]<\/a><\/p>\n\n\n\n

12. Alison L. Gibbs and Francis Edward Su. On choosing and bounding probability metrics.
International Statistical Review,<\/em> 70(3):419\u2013435, 2002.
arXiv:math\/0209021<\/a> Version February 2002.<\/p>\n\n\n\n

11. Elisha Peterson* and Francis Edward Su. Four-Person Envy-Free Chore Division.
Math. Mag., <\/em>75(2):117\u2013122, 2002.
[PDF]<\/a><\/p>\n\n\n\n

10. 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.,<\/em> 19(4):723\u2013749, 2002.
[PDF]<\/a> This algorithm in this paper has been implemented in The Fair Division Calculator<\/a> (New York Times Version).<\/p>\n\n\n\n

9. Francis Edward Su. Discrepancy convergence for the drunkard’s walk on the sphere. 
Electron. J. Probab.,<\/em> 6:no. 2, 20 pp. (electronic), 2001.
[PDF]<\/a><\/p>\n\n\n\n

8. 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,<\/em> pages 21\u201336. The International Institute for Advanced Studies in Systems Research and Cybernetics, Windsor, Canada, 2000.
[PDF]<\/a><\/p>\n\n\n\n

7. Francis Edward Su. Reviews: Cake-Cutting Algorithms: Be Fair if You Can. 
Amer. Math. Monthly,<\/em> 107(2):185\u2013188, 2000.
[PDF]<\/a> [published version<\/a>]<\/p>\n\n\n\n

6. Francis Edward Su. A LeVeque-type lower bound for discrepancy. 
In Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA),<\/em> pages 448\u2013458. Springer, Berlin, 2000. 
[PDF]<\/a><\/p>\n\n\n\n

5. Arthur T. Benjamin, Francis Edward Su, and Jennifer J. Quinn. Counting on Continued Fractions. 
Math. Mag.,<\/em> 73(2):98\u2013104, 2000. 
[PDF]<\/a><\/p>\n\n\n\n

4. Arthur T. Benjamin, Jennifer J. Quinn, and Francis Edward Su. Phased tilings and generalized Fibonacci identities. 
Fibonacci Quart.,<\/em> 38(3):282\u2013288, 2000.
[PDF]<\/a><\/p>\n\n\n\n

3. Francis Edward Su. Rental harmony: Sperner’s lemma in fair division. 
Amer. Math. Monthly,<\/em> 106(10):930\u2013942, 1999.
[PDF]<\/a> This article was awarded the MAA’s 2001 Merten M. Hasse Prize<\/a> for mathematical exposition.<\/p>\n\n\n\n

2. Francis Edward Su. Convergence of random walks on the circle generated by an irrational rotation.
Trans. Amer. Math. Soc.,<\/em> 350(9):3717\u20133741, 1998.
[PDF]<\/a><\/p>\n\n\n\n

1. Francis Edward Su. Borsuk-Ulam implies Brouwer: a direct construction.
Amer. Math. Monthly,<\/em> 104(9):855\u2013859, 1997.
[PDF]<\/a><\/p>\n\n\n\n

0. Francis Edward Su. Methods for Quantifying Rates of Convergence for Random Walks on Groups. 
Ph.D. Thesis, Harvard University. Advisor: Persi Diaconis.<\/em><\/p>\n\n\n\n

\n\n\n\n

Not Yet Published<\/h2>\n\n\n\n

<\/p>\n\n\n\n

Roberto Barrera, Kathryn Nyman, Amanda Ruiz, Francis Edward Su, Yan X. Zhang, Discrete Envy-free Division of Necklaces and Maps.
arXiv:1510.02132<\/a><\/p>\n\n\n\n

Rosalie Carlson*, Stephen Flood, Kevin O’Neill*, and Francis Edward Su. A Turan-type theorem for circular arc graphs. 
<\/a>arXiv:1110.4205<\/a><\/p>\n\n\n\n

Claus-Jochen Haake and Francis Edward Su. Fair division procedures: why use Mathematics? 
In Procedural Approaches to Conflict Resolution<\/em> (Matthias Raith, ed.), to appear.
[PDF]<\/a><\/p>\n\n\n\n

Elisha Peterson* and Francis Edward Su. N-person envy-free chore division.
arXiv:0909.0303<\/a>  <\/p>\n\n\n\n

Kyle E. Kinneberg*, Aaron Mazel-Gee*, Tia Sondjaja*, and Francis Edward Su. A cubical antipodal theorem.
arXiv:0909.0471<\/a>  <\/p>\n\n\n\n

Sarah Fletcher*, Christopher Hardin, and Francis Edward Su. The agreement number of tree societies.<\/p>\n\n\n\n

\n\n\n\n

Other Writings<\/h2>\n\n\n\n

The Banach-Tarski Paradox.  An expository paper for my Minor Thesis<\/em> requirement, Harvard University. 
[PDF]<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

You can probably tell that my research interests have changed over the years. 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 […]<\/p>\n","protected":false},"author":9,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-215","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/pages\/215","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/comments?post=215"}],"version-history":[{"count":40,"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/pages\/215\/revisions"}],"predecessor-version":[{"id":1350,"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/pages\/215\/revisions\/1350"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/media?parent=215"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/su\/wp-json\/wp\/v2\/tags?post=215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}