We will consider the problem of elimination in communication complexity, that was first raised by Ambainis et al. and later studied by Beimel et al. for its connection to the famous direct sum question.

The isoperiemtric profile of a Graph is a function that measures, for an integer k, is the size of the smallest edge boundary over all sets of vertices of size k.

In 1977, J.A. Davis et al showed that any finite subset of natural numbers can be permuted such that it does not contain any 3-term A.P. as a sub-sequence. However, this is not true for the set of all natural numbers.

Peer reviewing is not just an important part of research, but also one of the main characteristics of scientific temper. However, over millions of years, we have evolved into selfish beings, and we attempt to maximize our benefits.

We consider the unbounded error communication complexity of XOR functions, i.e. those of the form f of XOR, where f is an arbitrary boolean function on n bits.