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Rectangular Arrays with Fixed Margins

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Part of the The IMA Volumes in Mathematics and its Applications book series (IMA,volume 72)

Abstract

In a variety of combinatorial and statistical applications, one needs to know the number of rectangular arrays of nonnegative integers with given row and column sums. The combinatorial problems include counting magic squares, enumerating permutations by descent patterns and a variety of problems in representation theory. The statistical problems involve goodness of fit tests for contingency tables. We review these problems along with the available techniques for exact and approximate solution.

Keywords

  • Random Walk
  • Span Tree
  • Contingency Table
  • Symmetric Function
  • Toric Variety

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Diaconis, P., Gangolli, A. (1995). Rectangular Arrays with Fixed Margins. In: Aldous, D., Diaconis, P., Spencer, J., Steele, J.M. (eds) Discrete Probability and Algorithms. The IMA Volumes in Mathematics and its Applications, vol 72. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0801-3_3

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  • DOI: https://doi.org/10.1007/978-1-4612-0801-3_3

  • Publisher Name: Springer, New York, NY

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