Counting and enumerating frequency tables with given margins

作者: Francesca Greselin

DOI:

关键词: Contingency tableMagic squareTable (information)Position (vector)Independence (probability theory)CombinatoricsColumn (database)PermutationClass (set theory)Discrete mathematicsMathematics

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

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