Re: Edges of polytopes

On Mar 5, 12:07 pm, "Michael Knudsen" <micknud...@xxxxxxxxx> wrote:
Hi,

I am reading the book "Algebraic Statistics for Computational Biology"
by Sturmfels and Pachter. They refer to the following result by
Gritzmann and Sturmfels:

Let P_1,P_2,...,P_k be polytopes in R^d, and let m denote the number
of non-parallel edges of P_1,P_2,...,P_k. Then the number of vertices
of the Minkowski sum P_1+P_2+...+P_k is at most
\sum_{j=0}^{d-1}\binom{m-1}{j}.

My question is: What can non-parallel edges possibly mean? As an
example, what are the non-parallel edges of a square with vertices
(0,0), (0,1), (1,0), (1,1) and a triangle with vertices (0,0), (0,1),
(1,0)? I have no idea :-(

Thanks!

--
Michael Knudsen
Draw the square:
Parallel edges are (0,0) to (1,0) with (0,1) to (1,1),
and (0,0) to (1,0) with (1,0) to (1,1).
In a triangle, no parllel edges are.
kunzmilan



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