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Summary: Zonotopal Subdivisions of Cyclic Zonotopes
CHRISTOS A. ATHANASIADIS*
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
e-mail: athana@math.kth.se
(Received: September 1999)
Communicated by K. Strambach
Abstract. The cyclic zonotope n; d is the zonotope in Rd
generated byany ndistinct vectors of
the form 1; t; t2
; . . . ; tdÀ1
. It is proved that the re¢nement poset of all proper zonotopal sub-
divisions of n; d which are induced by the canonical projection p: n; dH
3 n; d, in
the sense of Billera and Sturmfels, is homotopy equivalent to a sphere and that any zonotopal
subdivision of n; d is shellable. The ¢rst statement gives an af¢rmative answer to the gener-
alized Baues problem in a new special case and re¢nes a theorem of Sturmfels and Ziegler
on the extension space of an alternating oriented matroid. An important ingredient in the proofs
is the fact that all zonotopal subdivisions of n; d are stackable in a suitable direction. It is
shown that, in general, a zonotopal subdivision is stackable in a given direction if and only if
acertain associatedoriented matroidprogram is Euclidean, inthesenseof Edmonds and Mandel.
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