The Smith normal form distribution of a random integer matrix
1 : Department of Mathematics
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Mathematics Department Columbia University Room 509, MC 4406 2990 Broadway New York, NY 10027 -
États-Unis
2 : Department of Mathematics [MIT]
Massachusetts Institute of Technology, Cambridge, Massachusetts -
États-Unis
We show that the density μ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities μps of SNF over Z/psZ with p a prime and s some positive integer. Our approach is to connect the SNF of a matrix with the greatest common divisors (gcds) of certain polynomials of matrix entries, and develop the theory of multi-gcd distribution of polynomial values at a random integer vector. We also derive a formula for μps and determine the density μ for several interesting types of sets.
| Subject : | : | Talk |
| Topics | : | Combinatorics |
| PDF version | : |  PDF version |
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