Dataset of Feasible, Edmonds' and Geographic Bi-vectors and Tri-vectors

The dataset consists of two sets of files in JSON format. Each file consists of an array of elements and each element is presented by a vector (it can be a bi-vector in the case of the first set or a tri-vector in the latter case). This vector is followed by the Euler characteristic of surface and a set of Edmonds’ realizations, described as a concatenation of two incidence matrices. Such bi-matrix gives rise to the corresponding graph, its dual, as well as one-to-one correspondence between their edges. The first set consists of 7 files, each containing all possible bi-vectors with all Edmonds’ realizations in a form of bi-matrices for a fixed ell (ranging from 2 to 7). The bi-vectors are stored in files with the value of ell at the end: edmonds-bi-vector-realization-ell2.json edmonds-bi-vector-realization-ell3.json edmonds-bi-vector-realization-ell4.json edmonds-bi-vector-realization-ell5.json edmonds-bi-vector-realization-ell6.json edmonds-bi-vector-realization-ell7.json The second set consists of 9 files, each containing all possible tri-vectors with all Edmonds’ realizations in a form of bi-matrices for a fixed ell (ranging from 2 to 8). The last file (for ell 9, contains only one Edmond’s realization per vector (if existing) due to time complexity). The tri-vectors are stored in files with the ell mentioned at the end: edmonds-tri-vector-realization-ell2.json edmonds-tri-vector-realization-ell3.json edmonds-tri-vector-realization-ell4.json edmonds-tri-vector-realization-ell5.json edmonds-tri-vector-realization-ell6.json edmonds-tri-vector-realization-ell7.json edmonds-tri-vector-realization-ell8.json edmonds-tri-vector-realization-ell9.json A set of utilities show use cases: Parsing functions with examples implemented in Sage: edmonds_import.sage Parsing functions with examples implemented in Java: EdmondsReaderBivector.java EdmondsReader.java本数据集包含两组JSON格式文件。每组文件均由元素数组构成，其中每个元素以向量形式表示：第一组文件对应的向量为双向量（bi-vector），第二组则为三向量（tri-vector）。每个向量后附带对应曲面的欧拉示性数（Euler characteristic），以及一组埃德蒙兹（Edmonds）实现结果，该实现以两个关联矩阵（incidence matrices）的拼接形式描述。此类双矩阵可生成对应的图及其对偶图，同时建立二者边之间的一一对应关系。 第一组共包含7个文件，每个文件存储了固定参数ℓ（取值范围为2至7）对应的所有可能双向量，以及以双矩阵形式呈现的全部埃德蒙兹实现结果。双向量存储文件的命名末尾带有对应ℓ的取值：edmonds-bi-vector-realization-ell2.json、edmonds-bi-vector-realization-ell3.json、edmonds-bi-vector-realization-ell4.json、edmonds-bi-vector-realization-ell5.json、edmonds-bi-vector-realization-ell6.json、edmonds-bi-vector-realization-ell7.json。 第二组共包含9个文件，每个文件存储了固定参数ℓ（取值范围为2至8）对应的所有可能三向量，以及以双矩阵形式呈现的全部埃德蒙兹实现结果。最后一个文件对应ℓ=9，受时间复杂度限制，该文件中每个向量仅包含至多一个埃德蒙兹实现结果（若存在）。三向量存储文件的命名末尾带有对应ℓ的取值：edmonds-tri-vector-realization-ell2.json、edmonds-tri-vector-realization-ell3.json、edmonds-tri-vector-realization-ell4.json、edmonds-tri-vector-realization-ell5.json、edmonds-tri-vector-realization-ell6.json、edmonds-tri-vector-realization-ell7.json、edmonds-tri-vector-realization-ell8.json、edmonds-tri-vector-realization-ell9.json。 本数据集附带一组实用工具，用于展示其使用场景：Sage语言实现的带示例解析函数：edmonds_import.sage；Java语言实现的带示例解析函数：EdmondsReaderBivector.java、EdmondsReader.java。