The problem of finding the number of rectangular tables of non-negative integers with given row and column sums occurs in many interesting contexts, mainly in combinatorial problems (counting magic squares, enumerating permutation by descents, etc.) and in statistical applications (studying contingency tables with given margins, testing for independence, etc.). In the present paper a new recursive argument is presented to produce a general expression for the number of m*n tables with given margins. The result has the same expressive force of the one presented by Gail and Mantel (1977), but, remarkably, the counting approach suggests, quite naturally, also a recursive algorithm to explicitly generate the entire class of tables. This work is a necessary step for studying a new measure of association, based on the relative position that a given table assumes in its class, endowed by an association ordering.

Greselin, F. (2003). Counting and enumerating frequency tables with given margins. STATISTICA & APPLICAZIONI, 1(2), 87-104.

### Counting and enumerating frequency tables with given margins

#### Abstract

The problem of finding the number of rectangular tables of non-negative integers with given row and column sums occurs in many interesting contexts, mainly in combinatorial problems (counting magic squares, enumerating permutation by descents, etc.) and in statistical applications (studying contingency tables with given margins, testing for independence, etc.). In the present paper a new recursive argument is presented to produce a general expression for the number of m*n tables with given margins. The result has the same expressive force of the one presented by Gail and Mantel (1977), but, remarkably, the counting approach suggests, quite naturally, also a recursive algorithm to explicitly generate the entire class of tables. This work is a necessary step for studying a new measure of association, based on the relative position that a given table assumes in its class, endowed by an association ordering.
##### Scheda breve Scheda completa Scheda completa (DC) Articolo in rivista - Articolo scientifico
Contingency tables, frequency tables, enumeration of contingency tables with given margins, counting contingency tables with given margins
English
2003
1
2
87
104
open
Greselin, F. (2003). Counting and enumerating frequency tables with given margins. STATISTICA & APPLICAZIONI, 1(2), 87-104.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/4643`
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