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Article No. eujc.1999.0319 Available online at http://www.idealibrary.com on
 

Summary: Article No. eujc.1999.0319
Available online at http://www.idealibrary.com on
Europ. J. Combinatorics (2000) 21, 19­47
Fiber Polytopes for the Projections between Cyclic Polytopes
CHRISTOS A. ATHANASIADIS, JES ŽUS A. DE LOERA, VICTOR REINER AND
FRANCISCO SANTOS
The cyclic polytope C(n, d) is the convex hull of any n points on the moment curve {(t, t2, . . . , td) :
t R} in Rd. For d > d, we consider the fiber polytope (in the sense of Billera and Sturmfels [6])
associated to the natural projection of cyclic polytopes : C(n, d ) C(n, d) which `forgets' the
last d - 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 ) for which the fiber polytope is canonical in either of the following two senses:
· all polytopal subdivisions induced by are coherent,
· 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 dimension.
c 2000 Academic Press
1. INTRODUCTION

  

Source: Athanasiadis, Christos - Department of Mathematics, University of Athens

 

Collections: Mathematics