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fTriangle -- determines the f-Triangle of a simplicial complex

Synopsis

Description

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

See also

Ways to use fTriangle :

For the programmer

The object fTriangle is a method function.