Communication Complexity of two Decision Problems

We observe that the communication complexity for deciding whether two permutations in Sn have a common inversion is log2(n!), and that for deciding whether two integers ⩽n are relatively prime is log2(6nΠ2)+O(n-12).

[1]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[2]  Michael E. Saks,et al.  Lattices, mobius functions and communications complexity , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.