Restricted Primitive Sets and Simplicial Subdivisions with Arbitrary Refinement Factors
Ludo Van der Heyden · Mathematics of Operations Research · 1982
We discuss the implementation of a refinement procedure for fixed point computations using Scarf's primitive sets. The procedure, presented in Van der Heyden (Van der Heyden, L. 1982. A Refinement procedure for computing fixed points using Scarf's primitive sets. Math. Oper. Res. 7 295–313.), moves between combinatorial objects called restricted primitive sets. We characterize restricted primitive sets when the vectors in these sets belong to a sequence of regular grids with increasing grid sizes. The refinement factor between successive grids is an arbitrary integer. These restricted primitive sets are associated with a set of easily implementable rules which guide the movement of the refinement procedure. We also present a geometrical interpretation of these restricted sets in terms of simplicial subdivisions.