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The Enumeration of Arrays and a Generalization Related to Contingency Tables by I.J. Good; J.F. Crook is a Computer Science article available to read on EtoBox.

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New methods are described for enumerating arrays, and for a gener;,lization t!iat is rqulred for a Bayesian analysis of contingency tables. Exact and approximate forrnlrilac ZT%C' given, together with some number-t heorctic results. ## 1. Iatroductiorh An array is a rectangte of non-negative integers, or the natu :ai generalization in more than two dimensions. We assume that an array is twc-dirnens!ianaI unless otherwise stated. We shall be concerned with the problem of enumerating arrays with assigned marginal totals and with a more general prcTblem related to the Bay&an analysis of contingency tables. The enumeration of arrays has received a fair amount of attention; see, for example, MacMahon [17], Anand, Dumir, and Gupta [2], Cariita [3,4], Crimson [ 123, Gupta [13], Gupta and N;ith IN], Abramson and Moser [I], Stein and Stein 1223, Stanley [21], and Good f IO], and work cited in those papers. We shall not be coi?cerned with "symmetrical" arrays bec;au!;e, apart from the combinatorial interest, KC are anxious to apply the results SO con!ingencp tables and these are not usually symmetrical, although some are, for exam+. Good [ 9, pa SS]. Denote the numbers of rows and columns of

Who reads The Enumeration of Arrays and a Generalization Related to Contingency Tables?

Author

I.J. Good; J.F. Crook

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0012-365X)

Published

1977

Language

EN

Field

Computer Science (Physical Sciences)