pureBetti(List) -- list of smallest integral Betti numbers corresponding to a degree sequence

Synopsis

Function: pureBetti
Usage:

pureBetti L
Inputs:
- L, a list, of strictly increasing integers
Outputs:
- a list, a list of the minimal integral Betti numbers which satisfy the Herzog-Kuhl equations

Description

The numerator P(t) of the Hilbert function of a module whose free resolution has a pure resolution of type L has the form P(t) = b_0 t^(d_0) - b_1 t^(d_1) + ... + (-1)^c b_c t^(d_c), where L = {d_0, ..., d_c}. If (1-t)^c divides P(t), as in the case where the module has codimension c, then the b_0, ..., b_c are determined up to a unique scalar multiple. This routine returns the smallest positive integral solution of these (Herzog-Kuhl) equations.

i1 : pureBetti{0,2,4,5}

o1 = {3, 10, 15, 8}

o1 : List

i2 : pureBetti{0,3,4,5,6,7,10}

o2 = {1, 50, 175, 252, 175, 50, 1}

o2 : List

Ways to use this method: