Definition 3.1 in [BW-1] defines the f-Triangle, a generalisation of the f-Vector, to have entries $f#(i,j)$ equal to the number of faces of $S$ with degree $i$ and dimension $j-1$. The degree of a face is the dimension of the largest face of $S$ containing it, plus one.
If $S$ is pure, then the last row is the traditional f-Vector and the remainder is zeros.
i1 : R = QQ[a..e]; |
i2 : fTriangle simplicialComplex {a*b*c, c*d*e, a*d, a*e, b*d, b*e} o2 = Tally{(2, 2) => 4} (3, 0) => 1 (3, 1) => 5 (3, 2) => 6 (3, 3) => 2 o2 : Tally |
i3 : fTriangle simplicialComplex {a*b*c*d*e} o3 = Tally{(5, 0) => 1 } (5, 1) => 5 (5, 2) => 10 (5, 3) => 10 (5, 4) => 5 (5, 5) => 1 o3 : Tally |
The object fTriangle is a method function.