3
$\begingroup$

This is related to one that I asked earlier:

The intersection of two $l_1$ balls

My question: are there any general classes of polytopes $P_1,P_2\subset\mathbb{R}^n$ such that $P_1$ has few vertices, $P_2$ has few vertices, and $P_1\cap P_2$ has few vertices? (in my particular problem, $P_1$ is a unit ball in the $l_1$ norm, but I am interested in this question more generally)

Improve this question
$\endgroup$
7
  • $\begingroup$ The unit ball is not a polytope. $\endgroup$
    – Richard Stanley
    Commented Apr 2, 2015 at 22:19
  • $\begingroup$ Meant to say "unit ball in $l_1$", how embarassing... $\endgroup$
    – Jennifer Gao
    Commented Apr 2, 2015 at 22:28
  • 2
    $\begingroup$ Welcome to MathOverflow! Perhaps they will make a "Human" badge for "edit on first post". Gerhard "Has Plenty Of Badges Already" Paseman, 2015.04.02 $\endgroup$
    – Gerhard Paseman
    Commented Apr 2, 2015 at 22:31
  • $\begingroup$ You question suggests this (easier) one: What is the maximum number of vertices of an intersection of two simplices in $\mathbb{R}^n$? $\endgroup$
    – Joseph O'Rourke
    Commented Apr 3, 2015 at 1:16
  • $\begingroup$ @JenniferGao: no problem. It's a nice question. $\endgroup$
    – Richard Stanley
    Commented Apr 3, 2015 at 1:47

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .