The h-vector of a Gorenstein set of points in a possibly bi-dominant corrspondence have according to Proposition 4.1 of Twenty Points in P^3 one of the following two types
I) {1,3,...,binomial(s+1,2),binomial(s+1,2)+c,binomial(s+1,2),...,3,1}
II) {1,3,...,binomial(s+1,2),binomial(s+1,2)+c,binomial(s+1,2)+c,binomial(s+1,2),...,3,1}
i1 : (L1,L2)=listhVectors 2 o1 = ({{1, 1, 1}, {1, 2, 1}, {1, 3, 1}, {1, 3, 3, 3, 1}, {1, 3, 4, 3, 1}, {1, ------------------------------------------------------------------------ 3, 5, 3, 1}, {1, 3, 6, 3, 1}}, {{1, 1}, {1, 1, 1, 1}, {1, 2, 2, 1}, {1, ------------------------------------------------------------------------ 3, 3, 1}, {1, 3, 3, 3, 3, 1}, {1, 3, 4, 4, 3, 1}, {1, 3, 5, 5, 3, 1}, ------------------------------------------------------------------------ {1, 3, 6, 6, 3, 1}}) o1 : Sequence |
i2 : apply(L1,hV-> dimFormula hV) o2 = {7, 11, 15, 23, 27, 31, 35} o2 : List |
i3 : apply(L2,hV->dimFormula hV) o3 = {6, 8, 14, 21, 26, 31, 37, 44} o3 : List |