Generate the j-th differential of a Kustin-Miller resolution of length g. So, e.g., for j=1 we obtain the relations of the ring resolved and for j=2 the first syzygies of those.
We use the notation of Section 2.3 of
J. Boehm, S. Papadakis: On the structure of Stanley-Reisner rings associated to cyclic polytopes, http://arxiv.org/abs/0912.2152 [math.AC]
For any j the last entry of L should be the variable T.
For j=1 we assume L = {b1, beta1, a1, T }.
For j=2 we assume L = {b2, beta2, h1, a2, alpha1, T }.
For j=3,...,g-1 we assume L = {bj, betaj, hj-1, aj, alphaj-1, bj-1, T }.
For j=g-1 we assume L = {betag-1, hg-1, ag-1, alphag-2, bg-2, T }.
For j=g we assume L = {alphag-1, ag, bg-1, u, T }.
Finally s equals k1-k2.