$\u0004$=2 SUSY 与六-五-立体-长方-截角 7-单纯形
$\cal N$=2 SUSY and the Hexipentisteriruncicantitruncated 7-Simplex
AI总结：
本文提出由 N=1 离壳超多重矩阵递归构造任意 N-扩展超多重态的算法，借助排列多面体、跳跃算子和截角结构刻画其顶点划分与面生成规律。
摘要：
我们研究在给定离壳 N = 1 超多重矩阵的最小矩阵表示时，递归创建任意 N-扩展“超多重态”的算法。通过利用截角和色数的概念，我们观察到图论中的着色顶点问题与排列多面体中不同超多重态集合的位置之间存在联系。我们引入并构造了“跳跃算子”这一概念，随后用其划分排列多面体的 8! 个顶点。我们明确地将这些顶点划分为 5,040 个八重组，其在排列多面体上的位置受到幻数规则约束。该递归构造中的布尔因子被证明服从双偶二元翻转规则。尽管这些跳跃算子通常并不构成置换群的正规子群，但我们发现存在“ab-正规陪集”，其中相同的左跳跃子和右跳跃子作为无序集合出现。最后，利用计算机模拟，我们研究了高阶排列多面体上可能产生低阶超多重态的各类面。
英文摘要：
We study algorithms for recursively creating arbitrary N-extended `supermultiplets' given minimal matrix representations of off-shell, N = 1 supermultiplet matrices. We observe connections between the color vertex problems in graph theory and the different supermultiplet sets locations in the permutahedron by using the concepts of truncation and chromatic number. The concept of `hopping operators' is introduced, constructed, and then used to partition the 8! vertices of the permutahedron. We explicitly partition these into 5,040 octets constrained in locations on the permutahedron by a magic number rule. Boolean factors in this recursive construction are shown to obey a doubly even binary flip rule. Although these hopping operators do not generally constitute normal subgroups of the permutation group, we find that `ab-normal cosets' exist where the same left- and right-hoppers appear as unordered sets. Finally, using computer simulations, we investigate the types of faces on higher-order permutahedron which may give rise to lower-order supermultiplets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
