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GlicciPointsInP3 :: listhVectors

listhVectors -- list all admissible h-vectors of Gorenstein points up to b

Synopsis

Description

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}

with 0 ≤c ≤s+1. The function creates the two list consisting of all h-vectors as above with s≤b.
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

Ways to use listhVectors :