Our results are most cleanly expressed in terms of the (arithmetic) coboundary polynomial, which is the following simple transformation of the (arithmetic) Tutte polynomial:
Clearly, the (arithmetic) Tutte polynomial can be recovered readily from the (arithmetic) coboundary polynomial.
Our formulas are conveniently expressed in terms of the exponential generating functions for the coboundary polynomials:
The finite field method is cleanly expressed in terms of the arithmetic coboundary polynomial:
G](x, y) in terms of the two variable coboundary
We view the coboundary
map [delta] as a map from the chain space of P to itself, which takes chains of length d to chains of length d +1 for all d.
We denote the simplicial boundary and coboundary
maps respectively by
bar] denotes Crapo's coboundary polynomial(iv); see [MR05, p.
This formula may be obtainable from the generating function for the coboundary polynomials of complete graphs, as computed by Ardila [Ard07, Thm.
2]) coincide with the boundary and coboundary
maps [[partial derivative].