  We show that a Boolean degree $d$ function on the slice $\binom{[n]}{k} = \{
(x_1,\ldots,x_n) \in \{0,1\} : \sum_{i=1}^n x_i = k \}$ is a junta, assuming
that $k,n-k$ are large enough. This generalizes a classical result of Nisan and
Szegedy on the hypercube. Moreover, we show that the maximum number of
coordinates that a Boolean degree $d$ function can depend on is the same on the
slice and the hypercube.
