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Rectangular Arrays with Fixed Margins

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Discrete Probability and Algorithms

Part of the book series: The IMA Volumes in Mathematics and its Applications ((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.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, Harvard University, Cambridge, 02138, MA, USA

    Persi Diaconis

  2. Silicon Graphics, 2011 N. Shoreline Blvd., Mount View, CA, 94043-1389, USA

    Anil Gangolli

Authors
  1. Persi Diaconis
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  2. Anil Gangolli
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Editor information

Editors and Affiliations

  1. Department of Statistics, University of California, Berkeley, CA, 94720, USA

    David Aldous

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Persi Diaconis

  3. Department of Computer Science Courant Institute, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Joel Spencer

  4. Department of Statistics, The Wharton School University of Pennsylvania, 3000 Steinberg Hall-Dietrich Hall, Philadelphia, PA, 19104-6302, USA

    J. Michael Steele

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© 1995 Springer Science+Business Media New York

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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

  • Print ISBN: 978-1-4612-6905-2

  • Online ISBN: 978-1-4612-0801-3

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