We assume that X is totally unimodular with respect to [LAMBDA], i.
Let X C A C U = Rd be a list of vectors that is totally unimodular. Let f be a real valued function on [Z.sub.-](X), the set of interior lattice points of the zonotope defined by X.
The Ehrhart polynomial of a zonotope that is defined by a totally unimodular matrix is also an evaluation of the Tutte polynomial (see e.
WLOG every totally unimodular list of vectors in R1 can be written in this way.
Since X is totally unimodular, [LAMBDA]/x [subset or equal to] U/x is a lattice for every x [member of] X and X/x is totally unimodular with respect to this lattice.
Theorem 4.6 (,Theorem 5.20) A matrix Y is called totally unimodular if each square submatrix of Y has determinant equal to 0, + 1 or - 1.
Corollary 4.9 A matrix Y defining a fine mixed cell T in n[[DELTA].sub.d-1] is totally unimodular.
From the way the projection was defined, it is enough to show that the matrix Y' defining a cell in n[[DELTA]'.sub.d-1] is totally unimodular. If there are two rows in Y' such that their support sets are incomparable, but not disjoint, the previous lemma tells us that there is a cycle in T of length [greater than or equal to] 4.
And Y is a totally unimodular matrix due to Corollary 4.9.