# hilbertSequence -- compute the Hilbert sequence of a given ideal in an exterior algebra

## Synopsis

• Usage:
hilbertSequence I
• Inputs:
• I, an ideal of an exterior algebra E
• Outputs:
• a list, nonnegative integers representing the Hilbert sequence of the quotient E/I

## Description

Given sum{h_i t^i}, i=1..n the Hilbert series of a graded K-algebra E/I, the sequence (1, h_1, ..., h_n) is called the Hilbert sequence of E/I.

Example:

 i1 : E=QQ[e_1..e_4,SkewCommutative=>true] o1 = E o1 : PolynomialRing, 4 skew commutative variables i2 : hilbertSequence ideal {e_1*e_2,e_2*e_3*e_4} o2 = {1, 4, 5, 1, 0} o2 : List i3 : hilbertSequence ideal {e_2*e_3*e_4} o3 = {1, 4, 6, 3, 0} o3 : List

## Ways to use hilbertSequence :

• "hilbertSequence(Ideal)"

## For the programmer

The object hilbertSequence is .