Volume 15, No 3, 2008, P. 74-90

UDC 519.852
V. N. Shevchenko, D. V. Gruzdev
About $f$-vectors of pyramidal triangulations of point configurations

Abstract:
A triangulation of a point configuration is called pyramidal if all its simplexes have a common vertex. Some inequalities for the components of the $f$-vectors of pyramidal triangulations were established. Moreover, for each $d>3$ there was constructed a $d$-dimensional polytope with its triangulation $T(d)$ such that the $f$-vector of $T(d)$ is not realizable as the $f$-vector of a pyramidal triangulation.
Bibl. 13.

Keywords: pyramidal triangulation, triangulation, point configuration.

Shevchenko Valery Nikolaevich ¹
Gruzdev Dmitry Valentinovich ¹
1. N. I. Lobachevski State University of Nizhni Novgorod,
ave. Gagarina, 23, 603950 Nizhni Novgorod, Russia
e-mail: shevgru@mail.ru, shev@uic.nnov.ru, gruzdevdv@mail.ru