EN|RU 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 © Sobolev Institute of Mathematics, 2015