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

Abstract

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

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