Abstract
In this paper discrete quasi-copulas (defined on a square grid I n 2 of [ 0 , 1 ] 2 ) are studied and it is proved that they can be represented by means of a special class of matrices with entries in [ - 1 , 1 ] . Special considerations are made for the case of irreducible discrete quasi-copulas (those with range I n ), showing that they can be represented through alternating-sign matrices and that they generate all discrete quasi-copulas through convex sums. In the process, the number of irreducible quasi-copulas on I n is given and those functions δ for which there exists a unique copula with δ as its diagonal section are characterized.
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