Fiber Polytopes For The Projections Between Cyclic Polytopes (1997)
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BibTeX
@MISC{Athanasiadis97fiberpolytopes,
author = {Christos Athanasiadis and Jesús A. de Loera and Victor Reiner and Francisco Santos},
title = {Fiber Polytopes For The Projections Between Cyclic Polytopes},
year = {1997}
}
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Abstract
The cyclic polytope C(n; d) is the convex hull of any n points on the moment curve f(t; t 2 ; : : : ; t d ) : t 2 Rg in R d . For d 0 ? d, we consider the fiber polytope (in the sense of Billera and Sturmfels) associated to the natural projection of cyclic polytopes : C(n; d 0 ) ! C(n; d) which "forgets" the last d 0 \Gamma d coordinates. It is known that this fiber polytope has face lattice indexed by the coherent polytopal subdivisions of C(n; d) which are induced by the map . Our main result characterizes the triples (n; d; d 0 ) for which the fiber polytope is canonical in either of the following two senses: ffl all polytopal subdivisions induced by are coherent, ffl the structure of the fiber polytope does not depend upon the choice of points on the moment curve. We also discuss a new instance with a positive answer to the Generalized Baues Problem, namely that of a projection : P ! Q where Q has only regular subdivisions and P has two more vertices than its...
