DOAJ Open Access 2020

The Smith normal form distribution of a random integer matrix

Yinghui Wang Richard P. Stanley

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (2)

Yinghui Wang

Richard P. Stanley

Format Sitasi

APA MLA BibTeX

Wang, Y., Stanley, R.P. (2020). The Smith normal form distribution of a random integer matrix. https://doi.org/10.46298/dmtcs.6352

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6352

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6352
Akses: Open Access ✓