Math Sciences

Square free Erdos-Selfridge Problem

Supplemental material for the paper The Erdős-Selfridge problem with square-free moduli by Paul Balister, Béla Bollobás, Robert Morris, Julian Sahasrabudhe, and Marius Tiba.

C Source code to check a suitable initial probability distribution can be found on [3]×[5]×[7]×[11]. This code uses the Gurobi Optimizer to solve multiple linear programming problem instances. See code for documentation.
Output of the above program listing all configurations with bounds >9.018.
C Source code to optimize the δ_k, k = 6,...,21, and check that the bounds provided by the first program are sufficient. This is a small, portable stand-alone C program.
C source code to determine necessary bound on f₂₁ in Corollary 5.2, and to also reproduce Table 1 in On the Erdős Covering Problem: the density of the uncovered set.
Output of the above program.