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

<p>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&rsquo; 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.</p> <p>The first set consists of 7 files, each containing all possible bi-vectors with all Edmonds&rsquo; realizations in a form of bi-matrices for a fixed ell (ranging from 2 to 7).</p> <p>The bi-vectors are stored in files with the value of ell&nbsp;at the end:</p> <ul> <li>edmonds-bi-vector-realization-ell2.json</li> <li>edmonds-bi-vector-realization-ell3.json</li> <li>edmonds-bi-vector-realization-ell4.json</li> <li>edmonds-bi-vector-realization-ell5.json</li> <li>edmonds-bi-vector-realization-ell6.json</li> <li>edmonds-bi-vector-realization-ell7.json</li> </ul> <p>The second set consists of 9 files, each containing all possible tri-vectors with all Edmonds&rsquo; realizations in a form of bi-matrices for a fixed ell (ranging from 2 to 8). The last file&nbsp;(for ell 9, contains only one Edmond&rsquo;s realization per vector (if existing) due to time complexity).</p> <p>The tri-vectors are stored in files with the ell mentioned at the end:</p> <ul> <li>edmonds-tri-vector-realization-ell2.json</li> <li>edmonds-tri-vector-realization-ell3.json</li> <li>edmonds-tri-vector-realization-ell4.json</li> <li>edmonds-tri-vector-realization-ell5.json</li> <li>edmonds-tri-vector-realization-ell6.json</li> <li>edmonds-tri-vector-realization-ell7.json</li> <li>edmonds-tri-vector-realization-ell8.json</li> <li>edmonds-tri-vector-realization-ell9.json</li> </ul> <p>A set of utilities show use cases:</p> <ul> <li> <p>Parsing functions with examples implemented in Sage:</p> </li> </ul> <p>edmonds_import.sage</p> <ul> <li> <p>Parsing functions with examples implemented in Java:</p> </li> </ul> <p>EdmondsReaderBivector.java</p> <p>EdmondsReader.java</p>