  We show that J_n, the Stanley-Reisner ideal of the n-cycle, has a free
resolution supported on the (n-3)-dimensional simplicial associahedron A_n.
This resolution is not minimal for n > 5; in this case the Betti numbers of J_n
are strictly smaller than the f-vector of A_n. We show that in fact the Betti
numbers of J_n are in bijection with the number of standard Young tableaux of
shape (d+1, 2, 1^{n-d-3}). This complements the fact that the number of
(d-1)-dimensional faces of A_n are given by the number of standard Young
tableaux of (super)shape (d+1, d+1, 1^{n-d-3}); a bijective proof of this
result was first provided by Stanley. An application of discrete Morse theory
yields a cellular resolution of J_n that we show is minimal at the first
syzygy. We furthermore exhibit a simple involution on the set of associahedron
tableaux with fixed points given by the Betti tableaux, suggesting a Morse
matching and in particular a poset structure on these objects.
