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References

  1. Aldous, D. and Diaconis, P. (1999). Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem. Bulletin of the American Mathematical Society (New Series) 36 413-432. MR2000g:60013
  2. Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998). Records. John Wiley & Sons, Inc., New York. MR2000b:60127
  3. Bai, Z.-D., Chao, C.-C., Hwang, H.-K. and Liang, W.-Q. (1998). On the variance of the number of maxima in random vectors and its applications. Annals of Applied Probability 8 886-895. MR99f:60019
  4. Bai, Z.-D., Hwang, H.-K., Liang, W.-Q. and Tsai, T.-H. (2000) Limit theorems for the number of maxima in random samples from planar regions. Technical Report C-2000-05 , Institute of Statistical Science, Academia Sinica, Taiwan.
  5. Baik, J. and Rains, E. M. (1999). The asymptotics of monotone subsequences of involutions. preprint, 59 pages.
  6. Barndorff-Nielsen, O. and Sobel, M. (1966). On the distribution of the number of admissible points in a vector random sample. Theory of Probability and its Applications 11 249-269. MR34:6819
  7. Baryshnikov, Y. M. (1987) The distribution of the number of nondominating variants. Soviet Journal of Computer and Systems Sciences 24 107-111; translated from Izvestiya Akademii Nauk SSSR. Tekhnicheskaya Kibernetika, 47-50 (1986).MR88i:60165
  8. Baryshnikov, Y. (2000) Supporting-points processes and some of their applications. Probability Theory and Related Fields 117 163-182. MR1771659
  9. Becker,R. A., Denby, L., McGill, R. and Wilks, A. R. (1987). Analysis of data from Places Rated Almanac. American Statistician 41 169-186.
  10. Bentley, J. L., Clarkson, L. L. and Levine, D. B. (1993). Fast linear expected-time algorithms for computing maxima and convex hulls. Algorithmica 9 168-183. MR93m:68161
  11. Blair, C. (1986). Random linear programs with many variables and few constraints. Mathematical Programming 34 62-71. MR88a:90123
  12. Bollobás, B. and Winkler, P. (1988). The longest chain among random points in Euclidean space. Proceedings of the American Mathematical Society 103 347-353. MR89k:60011
  13. Buchta, C. and Reitzner, M. (1997). Equiaffine inner parallel curves of a plane convex body and the convex hulls of randomly chosen points. Probability Theory and Related Fields 108 385-415. MR98f:52002
  14. Bühlmann, H. (1970). Mathematical Methods in Risk Theory. Die Grundlehren der mathematischen Wissenschaften, Band 172, Springer-Verlag, New York. MR97k:62213
  15. Chow, Y. S. and Teicher, H. (1978). Probability Theory: Independence, Interchangeability, Martingales. Springer-Verlag, New York. MR98e:60003
  16. Datta, A., Maheshwari, A. and Sack, J.-R. (1996). Optimal parallel algorithms for direct dominance problems. Nordic Journal of Computing 3 72-88. MR97d:68234
  17. Devroye, L. (1980). A note on finding convex hulls via maximal vectors. Information Processing Letters 11 53-56. MR82a:68070
  18. Devroye, L. (1986). Lecture Notes on Bucket Algorithms. Birkh"auser Boston, Boston, MA. MR88m:68003
  19. Devroye, L. (1993). Records, the maximal layer, and uniform distributions in monotone sets. Computers and Mathematics with Applications 25 19-31. MR94f:60015
  20. Devroye, L. (1999). A note on the expected time for finding maxima by list algorithms. Algorithmica 23 97-108. MR99m:60071
  21. Dwyer, R. (1990). Kindler, gentler, average-case analysis for convex hulls and maximal vectors. SIGACT News 21 64-71.
  22. Elster, K.-H. (Ed.) (1993). Modern Mathematical Methods of Optimization. Akademie Verlag, Berlin; translated from the Russian by B. Luderer. MR95d:90004
  23. Flajolet, P. and Sedgewick, R. (1995). Mellin transforms and asymptotics: finite differences and Rice's integrals. Theoretical Computer Science 144 101-124. MR96i:39003
  24. Frieze, A. and Pittel, B. G. (1995). Probabilistic analysis of an algorithm in the theory of markets in indivisible goods. Annals of Applied Probability 5 768-808. MR96j:90025
  25. Golin, M. J. (1993). Maxima in convex regions. in Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms , (Austin, TX, 1993), 352-360, ACM, New York. MR93m:90059
  26. Güting, R. H., Nurmi, O. and Ottmann, T. (1989). Fast algorithms for direct enclosures and direct dominances. Journal of Algorithms 10 170-186. MR90j:90075
  27. Harsanyi, J. C. (1988). Rational Behavior and Bargaining Equilibrium in Games and Social Situations . Cambridge University Press, Cambridge; Reprint of the 1986 edition. MR89e:90032
  28. Hwang, H.-K. (1998) On convergence rates in the central limit theorems for combinatorial structures. European Journal of Combinatorics 19 329-343. MR99c:60014
  29. Hwang, H.-K. (1999). Asymptotics of Poisson approximation to random discrete distributions: an analytic approach. Advances in Applied Probability 31 448-491. MR2000k:60054
  30. Johnson, N. L., Kotz, S. and Kemp, A. (1992). Univariate Discrete Distributions. Second edition, John Wiley & Sons, New York. MR95d:62018
  31. Karlin, S. (1959). Mathematical Methods and Theory in Games, Programming and Economics, Volume I: Matrix Games, Programming, and Mathematical Economics. Addison-Wesley, Reading, Mass. MR93a:90001
  32. Leitmann, G. and Marzollo, A. (Eds.) (1975). Multicriteria Decision Making. Springer-Verlag, New York. MR56:4862
  33. Preparata, F. P. and Shamos, M. I. (1985). Computational Geometry: An Introduction. Springer-Verlag, New York. MR87d:68102
  34. Rényi, A. (1962). Théorie des éléments saillants d'une suite d'observations. Ann. Fac. Sci. Univ. Clermont-Ferrand No. 8 , 7-13; also in Selected papers of Alfréd Rényi, Volume III: 1962-1970, Edited by Pál Turán, Akadémiai Kiadó, Budapest (1976). MR44:3376
  35. Rényi, A. and Sulanke, R. (1963). Über die konvexe Hülle von n zufällig gewählten Punkten. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 75-84. MR27:6190
  36. Sholomov, L. A. (1984). Survey of estimational results in choice problems. Engineering Cybernetics 21 51-75. MR85c:90002
  37. Stadler, W. (Ed.) (1988). Multicriteria Optimization in Engineering and in the Sciences. Plenum Press, New York. MR89f:90171
  38. Steuer, R. E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. John Wiley & Sons, New York. MR87h:90235
  39. Zeleny, M. (1974). Linear Multiobjective Programming. Lecture Notes in Economics and Mathematical Systems, Vol. 95, Springer-Verlag, Berlin-New York. MR50:3928
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