Junta threshold for low degree Boolean functions on the slice (Q2699646)

Summary: We show that a Boolean degree \(d\) function on the slice \(\binom{[n]}{k}\) is a junta if \(k \geqslant 2d\), and that this bound is sharp. We prove a similar result for \(A\)-valued degree \(d\) functions for arbitrary finite \(A\), and for functions on an infinite analog of the slice.