The local theorem for monotypic tilings.

Dolbilin, Nikolai; Schulte, Egon

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Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced...