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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums


Authors: Alexander Barvinok and J. A. Hartigan
Journal: Trans. Amer. Math. Soc. 364 (2012), 4323-4368
MSC (2010): Primary 05A16, 52B55, 52C07, 60F05
Published electronically: March 20, 2012
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Abstract: We count $ m \times n$ non-negative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as $ m$ and $ n$ grow.


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Additional Information

Alexander Barvinok
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
Email: barvinok@umich.edu

J. A. Hartigan
Affiliation: Department of Statistics, Yale University, New Haven, Connecticut 06520-8290
Email: john.hartigan@yale.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05585-1
PII: S 0002-9947(2012)05585-1
Received by editor(s): April 5, 2010
Received by editor(s) in revised form: March 11, 2011, and March 18, 2011
Published electronically: March 20, 2012
Additional Notes: The research of the first author was partially supported by NSF Grant DMS 0856640 and a United States–Israel BSF grant 2006377.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.