Consider a polynomial ring in N variables. For any hilbert function, there is a unique lexsegment ideal. Furthermore, this ideal has graded Betti numbers that are at least as large as those of any other ideal with that hilbert function.
The Hilbert function of a lexsegment ideal is determined by the values in the degrees that are at and below the largest degree of any generator. As a result, it makes sense to specify the Hilbert function through the largest degree of a generator and then truncate the rest of the function.
This function returns the graded Betti numbers of a lexsegment ideal with the given, tuncated, Hilbert function.
i1 : lexBetti (4, {1,2,3,3,3,3})
0 1 2 3
o1 = total: 1 3 3 1
0: 1 2 1 .
1: . . . .
2: . 1 2 1
o1 : BettiTally
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i2 : lexBetti (4, {1,2,3,3,3,3,0})
0 1 2 3 4
o2 = total: 1 6 12 10 3
0: 1 2 1 . .
1: . . . . .
2: . 1 2 1 .
3: . . . . .
4: . . . . .
5: . 3 9 9 3
o2 : BettiTally
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i3 : lexBetti (5, {1,5,15,35})
0
o3 = total: 1
0: 1
o3 : BettiTally
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