  Denote by p_k the k-th power sum symmetric polynomial n variables. The
interpretation of the q-analogue of the binomial coefficient as Hilbert
function leads us to discover that n consecutive power sums in n variables form
a regular sequence. We consider then the following problem: describe the
subsets n powersums forming a regular sequence. A necessary condition is that
n! divides the product of the degrees of the elements. To find an easily
verifiable sufficient condition turns out to be surprisingly difficult already
in 3 variables. Given positive integers a<b<c with GCD(a,b,c)=1, we conjecture
that p_a, p_b, p_c is a regular sequence for n=3 if and only if 6 divides abc.
We provide evidence for the conjecture by proving it in several special
instances.
