نقدم الآن خوارزمية تنتج قائمة التصنيف للبوليتوبات الفانو الناعمة لأي د. المدخل للخوارزمية هو رقم واحد، أي الرقم الصحيح الموجب. تم استخدام الخوارزمية لتصنيف البوليتوبات الفانو الناعمة لد<=7. هناك 7622 صنف من البوليتوبات الفانو الناعمة للد 6 و 72256 صنف من البوليتوبات الفانو الناعمة للد 7.
We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.
This paper is concerned with the extreme points of the polytopes of stochastic tensors. By a tensor we mean a multi-dimensional array over the real number field. A line-stochastic tensor is a nonnegative tensor in which the sum of all entries on each
We consider the problem of sampling from a density of the form $p(x) propto exp(-f(x)- g(x))$, where $f: mathbb{R}^d rightarrow mathbb{R}$ is a smooth and strongly convex function and $g: mathbb{R}^d rightarrow mathbb{R}$ is a convex and Lipschitz fu
In the chapter Magic with a Matrix in emph{Hexaflexagons and Other Mathematical
Let $K subset R^d$ be a smooth convex set and let $P_la$ be a Poisson point process on $R^d$ of intensity $la$. The convex hull of $P_la cap K$ is a random convex polytope $K_la$. As $la to infty$, we show that the variance of the number of $k$-dimen
Let $K$ be a convex body in $mathbb{R}^n$ and $f : partial K rightarrow mathbb{R}_+$ a continuous, strictly positive function with $intlimits_{partial K} f(x) d mu_{partial K}(x) = 1$. We give an upper bound for the approximation of $K$ in the symmet