@article{22190,
  abstract     = {We consider the set of 𝑚×𝑛 matrices with rational entries having numerator and denominator of size at most H and obtain various upper bounds on the number of such matrices of a given rank, or with a given determinant, or a given characteristic polynomial. We also consider similar questions for matrices whose entries are Egyptian fractions.},
  author       = {Afifurrahman, Muhammad and Kuperberg, Vivian Zieve and Ostafe, Alina and Shparlinski, Igor E.},
  issn         = {1435-5337},
  journal      = {Forum Mathematicum},
  number       = {4},
  publisher    = {De Gruyter},
  title        = {{Statistics of ranks, determinants and characteristic polynomials of rational matrices}},
  doi          = {10.1515/forum-2024-0114},
  volume       = {37},
  year         = {2024},
}