no code implementations • 26 Jan 2021 • Jonathan Turner, Ilias Kotsireas, Dursun Bulutoglu, Andrew Geyer
We provide a search method for Legendre pairs of composite length based on generating binary matrices with fixed row and column sums from compressed, complementary integer vectors.
Combinatorics 05B10 (Primary) 05B20 (Secondary) G.2.1
no code implementations • 8 Jan 2021 • Ilias Kotsireas, Christoph Koutschan
We prove a proposition that connects constant-PAF sequences and the corresponding Legendre pairs with integer PSD values.
Combinatorics
1 code implementation • 8 Dec 2020 • Curtis Bright, Kevin K. H. Cheung, Brett Stevens, Ilias Kotsireas, Vijay Ganesh
In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry$\unicode{x2014}$the long-standing problem of determining if a projective plane of order ten exists.
no code implementations • 9 Jul 2019 • Curtis Bright, Ilias Kotsireas, Vijay Ganesh
By combining the search power of SAT with the deep mathematical knowledge in CASs we can solve many problems in mathematics that no other known methods seem capable of solving.
no code implementations • 14 Jun 2019 • Curtis Bright, Jürgen Gerhard, Ilias Kotsireas, Vijay Ganesh
In this article we demonstrate how to solve a variety of problems and puzzles using the built-in SAT solver of the computer algebra system Maple.