Beck's Three Permutations Conjecture: A Counterexample and Some Consequences

@article{Newman2012BecksTP,
title={Beck's Three Permutations Conjecture: A Counterexample and Some Consequences},
author={Alantha Newman and Ofer Neiman and Aleksandar Nikolov},
journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science},
year={2012},
pages={253-262}
}

Given three permutations on the integers 1 through n, consider the set system consisting of each interval in each of the three permutations. In 1982, Beck conjectured that the discrepancy of this set system is O(1). In other words, the conjecture says that each integer from 1 through n can be colored either red or blue so that the number of red and blue integers in each interval of each permutations differs only by a constant. (The discrepancy of a set system based on two permutations is at… CONTINUE READING