Search Results for author: Ilias Kotsireas

Found 5 papers, 1 papers with code

Legendre pair of length $77$ using complementary binary matrices with fixed marginals

no code implementations26 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

Legendre pairs of lengths $\ell \equiv 0$ (mod $3$)

no code implementations8 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

A SAT-based Resolution of Lam's Problem

1 code implementation8 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.

SAT Solvers and Computer Algebra Systems: A Powerful Combination for Mathematics

no code implementations9 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.

Mathematical Proofs Mathematical Reasoning

Effective problem solving using SAT solvers

no code implementations14 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.

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