Publications (Julius Barbanel)

Return to Julius Barbanel’s faculty page.

Articles on Set Theory

  1. Supercompact cardinals, elementary embeddings, and fixed points, Journal of Symbolic Logic 47 (1982) 84–88.
  2. Supercompact cardinals and trees of normal ultrafilters, Journal of Symbolic Logic 47 (1982) 89–109.
  3. Many-times huge and superhuge cardinals (with C. A. DiPrisco and I. B. Tan), Journal of Symbolic Logic 49 (1984) 112–122.
  4. An ordering of normal ultrafilters, Fundamenta Mathematicae 125 (1985) 155–165.
  5. Supercompact cardinals, trees of normal ultrafilters, and the partition property, Journal of Symbolic Logic 51 (1986) 701–708.
  6. Flipping properties and huge cardinals, Fundamenta Mathematicae 132 (1989) 171–188.
  7. Making the hugeness of κ resurrectable after κ-directed closed forcing, Fundamenta Mathematicae 137 (1991) 9–24.
  8. Almost hugeness and a related notion, Notre Dame Journal of Formal Logic 32 (1991) 255–265.
  9. A note on a result of Kunen and Pelletier, Journal of Symbolic Logic 57 (1992) 461–465.
  10. On the relationship between the partition property and the weak partition property for normal ultrafilters on Pκλ, Journal of Symbolic Logic 58 (1993) 119–127.
  11. Some variations on the partition property for normal ultrafilters on Pκλ, Fundamenta Mathematicae 142 (1993) 163–171.

Articles on Fair Division

  1. Preference relations and measures in the context of fair division (with A. Taylor), Proceedings of the American Mathematical Society 123 (1995) 2061–2070.
  2. Game-theoretic algorithms for fair and strongly fair cake division with entitlements, Colloquium Mathematicum 69 (1995) 59–73.
  3. Super envy-free cake division and independence of measures, Journal of Mathematical Analysis and Applications 197 (1996) 54–60.
  4. Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division (with W. Zwicker), Theory and Decision 43 (1997) 203–207.
  5. On the possibilities for partitioning a cake, Proceedings of the American Mathematical Society 124 (1996) 3443–3451.
  6. Partition ratios, Pareto optimal cake division, and related notions, Journal of Mathematical Economics 32 (1999) 401–428.
  7. On the structure of Pareto optimal cake partitions, Journal of Mathematical Economics 33 (2000) 401–424.
  8. On the Geometry of Cake Division, Journal of Mathematical Analysis and Applications 264 (2001) 639–656.
  9. Cake division with minimal cuts: envy-free procedures for 3 persons, 4 persons, and beyond (with Steven J. Brams), Mathematical Social Sciences 48 (2004) 251–269.
  10. Cutting a Pie is not a Piece of Cake (with Steven J. Brams and Walter Stromquist), American Mathematical Monthly 116 (6) (2009) 496–514.
  11. A Geometric Approach to Fair Division, The College Mathematics Journal 41 (4) (2010), 268–280.
  12. Two-person Pie-cutting: The Fairest Cuts (with Steven J. Brams), The College Mathematics Journal 42 (1) (2011) 25–32.
  13. Two-Person Cake Cutting: The Optimal Number of Cuts (with Steven J. Brams), The Mathematical Intelligencer 36 (3) (2014) 23-35.

Books

  1. The Geometry of Efficient Fair Division, Cambridge, England: Cambridge University Press (2005).

Other

  1. A kinematic approach to the fundamental theorem of calculus, Journal of Undergraduate Mathematics and its Applications 20 (1999) 101–115.
  2. One model for an integrated math/physics course focusing on electricity and magnetism and related calculus topics (with J. Dunn), American Journal of Physics 68 (2000) 749–757.
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