  We outline a generalization of the Groebner fan of a homogeneous ideal with
maximal cells parametrizing truncated Groebner bases. This "truncated" Groebner
fan is usually much smaller than the full Groebner fan and offers the natural
framework for conversion between truncated Groebner bases. The generic Groebner
walk generalizes naturally to this setting by using the Buchberger algorithm
with truncation on facets. We specialize to the setting of lattice ideals. Here
facets along the generic walk are given by unique (facet) binomials. This along
with the representation of binomials as integer vectors give an especially
simple version of the generic Groebner walk. Computational experience with the
special Aardal-Lenstra integer programming knapsack problems is reported.
