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math.NT2010
Natural Density Distribution of Hermite Normal Forms of Integer Matrices
Gerard Maze
The Hermite Normal Form (HNF) is a canonical representation of matrices over any principal ideal domain. Over the integers, the distribution of the HNFs of randomly looking matrice…
math.NT2010
Natural Density of Rectangular Unimodular Integer Matrices
G. Maze, J. Rosenthal, U. Wagner
In this paper, we compute the natural density of the set of k x n integer matrices that can be extended to an invertible n x n matrix over the integers. As a corollary, we find the…