Small cones of oriented semi-metrics

Cones of weighted quasi-metrics, weighted quasi-hypermetrics and of oriented cuts

We show that the cone of weighted n-point quasi-metrics WQMet_n, the cone of weighted quasi-hypermetrics WHyp_n and the cone of oriented cuts OCut_n are projec- tions along an extreme ray of the metric cone Metn+1, of the hypermetric cone Hypn+1 and of the cut cone Cut_{n+1}, respectively. This projection is such that if one knows all faces of an original cone then one knows all faces of the projected cone.

Data mining for cones of metrics, quasi-metrics, hemi-metrics and super-metrics

Using some adaptations of the adjacency decomposition method \cite{CR} and the program {\it cdd} (~\cite{Fu}), we compute the first computationally difficult cases of convex cones of $m$-ary and oriented analogs of semi-metrics and cut semi-metrics, which were introduced in \cite{DR2} and \cite{DP}. We considered also more general notion of $(m,s)$-super-metric and corresponding cones. The data on related cones - the number of facets, of extreme rays, of their orbits and diameters - are collected in Table \ref{tab:MainLovelyTable}. We study also criterion of adjacency for skeletons of those co…

锥与约束彩色卡拉西奥多里定理

Cone and constrained colorful Carathéodory Theorems

本文在拓扑学上扩展霍尔姆森等人的方法，研究凸锥取代凸包及横截约束非由拟阵编码时的彩色卡拉西奥多里型结果，通过分析单纯复形同调群，如定向拟阵支撑复形，实现经典特弗伯格定理新扩展及方法精细应用。

从序到凸性：面理论与广义分离

Convexity from order: a theory of faces and generalized separation

本文从序理论视角研究凸集，将面视为强最小值集合，通过定向映射实现广义分离，并定义联合支撑子空间，在仅假设凸性下推广了面运算结果，解决了开放问题。