My Papers and Preprints (in Postscript and PDF formats)

Color scheme for paper themes:
            Papers on random walks and related issues are RED.
            Papers on fair division and related problems in geometric combinatorics are GREEN.
            Papers on miscellaneous topics are MAGENTA.
            Many papers have been jointly authored with Harvey Mudd undergraduates, who are starred*.
Some of these are also listed in the Claremont Economics Working Papers archive.
For a description of how my research interests evolved, click here.
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 PUBLISHED WORKS:

  1. Methods for Quantifying Rates of Convergence for Random Walks on Groups.
    Ph.D. Thesis, Harvard University, 1995.    Advisor: Persi Diaconis.
     
  2. Borsuk-Ulam implies Brouwer: a direct construction.
    Amer. Math. Monthly, 104(1997), pp. 855-859.
    [ Abstract ] [ Postscript ] [ PDF ]
     
  3. Convergence of random walks on the circle generated by an irrational rotation.
    Trans. Amer. Math. Soc., 350(1998), pp. 3717-3741.
    [Abstract] [ Postscript ] [ PDF ]
     
  4. Rental harmony: Sperner's lemma in fair division.
    Amer. Math. Monthly, 106(1999), pp. 930-942.
    This article was awarded the MAA's 2001 Merten M. Hasse Prize for mathematical exposition.
    [ Abstract ] [ Postscript ] [ PDF ]
     
  5. A LeVeque type lower bound for discrepancy.
    in Monte Carlo Methods and Quasi-Monte Carlo Methods 1998,
    H. Niederreiter and J. Spanier (eds.), Springer-Verlag, 2000, pp. 448-458.
    [Abstract] [ Postscript ] [ PDF ]
     
  6. Book Review: Cake-Cutting Algorithms by J. Robertson and W. Webb.
    Amer. Math. Monthly, 107(2000), pp. 185-188.
    [ Abstract ] [ Postscript ] [ PDF ]
     
  7. Phased tilings and generalized Fibonacci identities.
    (with Arthur Benjamin and Jennifer Quinn)
    Fibonacci Quarterly 38(2000), pp. 282-288.
    [ Abstract ]   [ Postscript ]  [ PDF ] 
     
  8. Counting on continued fractions.
    (with Arthur Benjamin and Jennifer Quinn) 
    Mathematics Magazine 73(2000), pp. 98-104.
    [ Abstract ]   [ Postscript ]  [ PDF ] 
     
  9. Procedural support for cooperative negotiations: theory and implementation.
    (with Matthias G. Raith) 
    Advances in Decision Technology and Intelligent Information Systems, Volume I (eds. Kurt J. Engemann and George E. Lasker),
    The International Institute for Advanced Studies in Systems Research and Cybernetics, Windsor, Canada, 2000, pp. 31-36.
    [Abstract]  [Postscript]  [PDF]
     
  10. Discrepancy convergence for the drunkard's walk on the sphere.
    Electronic Journal of Probability 6 (2001) no. 2, 1-20.
    [Abstract] [ Postscript ] [ PDF ]
     
  11. Four-person envy-free chore division.
    (with Elisha Peterson*)
    Mathematics Magazine 75(2002), pp. 117-122.
    [Abstract]   [ Postscript ] [ PDF ]
     
  12. Bidding for envy-freeness: a procedural approach to n-player fair division problems.
    (with Claus-Jochen Haake and Matthias G. Raith) 
    Social Choice and Welfare 19(2002), pp. 723-749.
    [ Abstract ] [ Postscript ] [ PDF ]
    The algorithm in this paper has been implemented in The Fair Division Calculator (Rent/"HRS" option).
     
  13. Random walks with badly approximable numbers.
    (with Doug Hensley)      
    Unusual Applications of Number Theory, 95-101,
    DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 64, Amer. Math. Soc., 2004.
    [Abstract] [Postscript] [PDF]
     
  14. Linear Recurrences through Tilings and Markov Chains.
    (with Christopher Hanusa* and Arthur Benjamin)
    Utilitas Mathematica 64(2003), pp. 3-17.
    [Abstract] [ Postscript ] [ PDF ]
    Version June 2001.
     
  15. On choosing and bounding probability metrics.
    (with Alison Gibbs)
    International Statistical Review (2002), vol. 70, number 3, 419-435.
    [Abstract]  [ Postscript ]  [PDF]
    Version February 2002.
     
  16. A polytopal generalization of Sperner's lemma.
    (with Jesus de Loera and Elisha Peterson*)
    J. Combinatorial Theory, Series A, 100 (2002), 1-26.
    [Abstract] [ Postscript ] [ PDF ]
     
  17. Consensus-halving via theorems of Borsuk-Ulam and Tucker.
    (with Forest Simmons)     
    Mathematical Social Sciences 45 (2003), 15-25.
    [Abstract] [ Postscript ] [ PDF ]
     
  18. Random walks on the torus with several generators.
    (with Timothy Prescott*)    ,
    Random Structures and Algorithms 25 (2004), 336-345. [Abstract and PDF at the arXiv:math.PR/0309011] Version April 2004.
     
  19. Lower bounds for simplicial covers and triangulations of cubes.
    (with Adam Bliss*)    ,
    Discrete and Computational Geometry 33 (2005), 669--686.
    [Abstract and PDF at the arXiv:math.CO/0310142]
     
  20. A constructive proof of Ky Fan's generalization of Tucker's lemma.
    (with Timothy Prescott*)    ,
    J. Combinatorial Theory, Series A 111 (2005), 257--265.
    [Abstract and PDF at the arXiv:math.CO/0310444].
     
  21. The LSB theorem implies the KKM lemma
    (with Gwen Spencer*)    ,
    Amer. Math. Monthly, 114(2007), 156--159.
    [Abstract and PDF at the arXiv:math.GN/0409092]
     
  22. The Shapley value of phylogenetic trees.
    (with Claus-Jochen Haake, Akemi Kashiwada*)    ,
    [Abstract and PDF at the arXiv:q-bio.QM/0506034]
    To appear, J. Mathematical Biology.
     
  23. A fixed point theorem for the infinite-dimensional simplex.
    (with Douglas Rizzolo*)    ,
    J. Math. Anal. Appl. 332(2007), 1063-1070.
    [Abstract and PDF at the arXiv:math.GN/0610707]
     
  24. Fair Division Procedures: Why use Mathematics?
    (with Claus-Jochen Haake)    ,
    Preprint. To appear in "Procedural Approaches to Conflict Resolution", M. Raith (ed.), Springer Verlag, forthcoming.
     
  25. Envy-free divisions with linked preferences.
    (with John Cloutier*)    ,
    Preprint.
     
  26. Algorithms for reconstructing phylogenetic trees from dissimilarity maps.
    (with Dan Levy, Ruriko Yoshida)    ,
    Preprint.
     
  27. A KKM theorem for trees and cycles.
    (with Andrew Niedermaier*)
    In progress.
     
  28. Minimal triangulations of simplotopes.
    (with Tyler Seacrest*)    ,
    In progress.
     
    Many of the above papers have been co-authored with Harvey Mudd undergraduates, who are starred*.

OTHER WRITINGS:
  • The Banach-Tarski Paradox.
    An expository paper for my Minor Thesis requirement, Harvard University, 1990.
    [Abstract] [ Postscript ] [ PDF ]
     
  • An upper bound for the relative entropy of Markov chains.
    A old technical report, 1997.
    [Abstract] [ Postscript ]
     
  • The cyclic mean of a periodic continued fraction.
    (with Andromeda Yelton*)  Results of an undergraduate research project, 1998.
    [Abstract]
     
  • Exact procedures for envy-free chore division.
    (with Elisha Peterson*)  Results of an undergraduate research project, 1998, some of which was published in "Four person envy-free division" above.
    [Abstract]   [ Postscript ]
     

    • last updated 2/2001
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