  The pinched Veronese poset $V^*_n$ is the poset with ground set consisting of
all non-negative integer vectors of length n such that the sum of their
coordinates is divisible by $n$ with exception of the vector $(1,...,1)$. For
two vectors $a$ and $b$ in $V^*_n$ we have $a \leq b$ if and only if $b - a$
belongs to the ground set of $V^*_n$.
  We show that every interval in $V^*_n$ is shellable for $n$ at least 4. In
order to obtain the result, we develop a new method for showing that a poset is
shellable. This method differs from classical lexicographic shellability.
  Shellability of intervals in $V^*_n$ has consequences in commutative algebra.
As a corollary we obtain a combinatorial proof of the fact that the pinched
Veronese ring is Koszul for $n \geq 4$. (This also follows from a result by
Conca, Herzog, Trung and Valla.)
