Computes the Betti bounds for complexes which are obtained by c-1 iterated stellar subdivisions from the boundary complex of a simplex on q+1 vertices.
The procedure can also be applied recursively to lists starting with the Betti numbers L={1,1} of a hypersurface.
The i-th entry of B corresponds to the bound of the i-th Betti number. For example, B#1 is the bound on the number of generators. The first and the last entry of B is always 1. The number of entries of B is c+1.
i1 : bettiBounds(1)
o1 = {1, 1}
o1 : List
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i2 : bettiBounds(2)
o2 = {1, 2, 1}
o2 : List
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i3 : bettiBounds(3)
o3 = {1, 5, 5, 1}
o3 : List
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i4 : bettiBounds(4)
o4 = {1, 11, 20, 11, 1}
o4 : List
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i5 : bettiBounds(5)
o5 = {1, 23, 62, 62, 23, 1}
o5 : List
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Alternatively one can also do:
i6 : L={1,1}
o6 = {1, 1}
o6 : List
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i7 : L=bettiBounds(L)
o7 = {1, 2, 1}
o7 : List
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i8 : L=bettiBounds(L)
o8 = {1, 5, 5, 1}
o8 : List
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i9 : L=bettiBounds(L)
o9 = {1, 11, 20, 11, 1}
o9 : List
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i10 : L=bettiBounds(L)
o10 = {1, 23, 62, 62, 23, 1}
o10 : List
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