Hi,
There are a few small things I would like to check with you before changing the files.
I notice a rather mixed notation for vectors. In most of the definitions x, x_1,... are elements of \mathbb{R}^n or similar. However,
1) in the definition of the combinations, we use p_1,...,p_k I think we should use x_1,...,x_k as in the rest of the user documentation.
2) in the definition of scalar product, x_1,...,x_n are the components of the vector x and, therefore elements of \mathhbb{R}. This is inconsistent with the rest of the paper.
I am trying to choose another letter for x_1,...,x_n and y_1,...,y_n for this definition. Note that b and c are already used for vectors. One possibility is to use \lambda_1,...,\lambda_n and \mu_1,...,\mu_n since \lambda is already used in the definition of the different combinations as elements of \mathbb{R} - and also in Minkowski's theorem.
ciao, Pat