Flag vectors of multiplicial polytopes

Details Flag vectors of multiplicial polytopes Flag vectors of multiplicial polytopes

2003-12-04

arxiv.org/abs/math/0312112v1

Mathematics

Combinatorics

12 pages, LaTeX

Scientific paper

Bisztriczky introduced the multiplex as a generalization of the simplex. A polytope is multiplicial if all its faces are multiplexes. In this paper it is proved that the flag vectors of multiplicial polytopes depend only on their face vectors. A special class of multiplicial polytopes, also discovered by Bisztriczky, is comprised of the ordinary polytopes. These are a natural generalization of the cyclic polytopes. The flag vectors of ordinary polytopes are determined. This is used to give a surprisingly simple formula for the h-vector of the ordinary d-polytope with n+1 vertices and characteristic k: h_i=binom{k-d+i}{i}+(n-k)binom{k-d+i-1}{i-1}, for i at most d/2. In addition, a construction is given for 4-dimensional multiplicial polytopes having two-thirds of their vertices on a single facet, answering a question of Bisztriczky.

Affiliated with

Also associated with

No associations

Rating

Flag vectors of multiplicial polytopes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Flag vectors of multiplicial polytopes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Flag vectors of multiplicial polytopes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-474889