The ideal of Pluecker relations has a quadratic Groebner basis. Under a suitable term order, the incomparable pairs of the poset P generate the initial ideal of the ideal of Pluecker relations.
Given two subsets S and T of 0,...,n-1, we partially order S ≤T if #S ≥#T and Si ≤Ti for all i from 1 to #T.
i1 : P = plueckerPoset 4; |
i2 : coveringRelations P o2 = {{{0}, {1}}, {{1}, {2}}, {{0, 1}, {0, 2}}, {{2}, {3}}, {{0, 2}, {0, 3}}, ------------------------------------------------------------------------ {{0, 2}, {1, 2}}, {{1, 2}, {1, 3}}, {{0, 1, 2}, {0, 1, 3}}, {{3}, {}}, ------------------------------------------------------------------------ {{0, 3}, {0}}, {{0, 3}, {1, 3}}, {{1, 3}, {2, 3}}, {{1, 3}, {1}}, {{0, ------------------------------------------------------------------------ 1, 3}, {0, 2, 3}}, {{0, 1, 3}, {0, 1}}, {{2, 3}, {2}}, {{0, 2, 3}, {0, ------------------------------------------------------------------------ 2}}, {{0, 2, 3}, {1, 2, 3}}, {{1, 2, 3}, {1, 2}}, {{0, 1, 2, 3}, {0, 1, ------------------------------------------------------------------------ 2}}} o2 : List |