  Inspired by recent results of Ein, Lazarsfeld, Erman and Zhou on the
non-vanishing of Betti numbers of high Veronese subrings, we describe the
behaviour of the Betti numbers of Stanley-Reisner rings associated with
iterated barycentric or edgewise subdivisions of a given simplicial complex.
Our results show that for a simplicial complex $\Delta$ of dimension $d-1$ and
for $1\leq j\leq d-1$ the number of $0$'s the j-th linear strand of the minimal
free resolution of the r-th barycentric or edgewise subdivision is bounded
above only in terms of $d$ and $j$ (and independently of $r$).
