The width of 5-dimensional prismatoids

Details The width of 5-dimensional prismatoids The width of 5-dimensional prismatoids

2012-02-21

arxiv.org/abs/1202.4701v1

Mathematics

Combinatorics

28 pages, 11 figures

Scientific paper

Santos' construction of counter-examples to the Hirsch conjecture is based on the existence of prismatoids of dimension d of width greater than d. The case d=5 being the smallest one in which this can possibly occur, we here study the width of 5-dimensional prismatoids, obtaining the following results: - There are 5-prismatoids of width six with only 25 vertices, versus the 48 vertices in Santos' original construction. This leads to lowering the dimension of the non-Hirsch polytopes from 43 to only 20. - There are 5-prismatoids with n vertices and width \Omega(n^(1/2)) for arbitrarily large n.

Affiliated with

Also associated with

No associations

Rating

The width of 5-dimensional prismatoids 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 The width of 5-dimensional prismatoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The width of 5-dimensional prismatoids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423947