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