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Community Bot
Community Bot
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This is related to one that I asked earlier:

The intersection of two $l_1$ ballsThe 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)

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)

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)

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Jennifer Gao
Jennifer Gao
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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)

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, but I am interested in this question more generally)

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)

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Jennifer Gao
Jennifer Gao
  • 131
  • 3

Polytopes whose intersections have few vertices

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, but I am interested in this question more generally)