Matroids.SelfDual
Item from PolyDB: This is a collection of identically self-dual (ISD) matroids of rank 2 to 5.
Raluca Vlad, Alheydis Geiger, Sachi Hashimoto, Bernd Sturmfels
Source code repository: https://github.com/sachihashimoto/self-dual
This is a collection of identically self-dual (ISD) matroids of rank 2 to 5. The data arose from the computations performed for the paper Self-dual matroids from canonical curves by Geiger, Hashimoto, Sturmfels and Vlad. The code for the computations can be found at https://github.com/sachihashimoto/self-dual, or https://mathrepo.mis.mpg.de/selfdual/index.html . This database contains a representative for each isomorphism class of an ISD matroid on at most 10 elements and rank equal to half the size of the ground set. Additionally to the usual matroid properties, the following data on the realization and self-dual realisation of the matroids over a field of characteristic zero is stored: Whether the matroid is realizable, the dimension of its realization space, whether the matroid is realizable by a self-dual point configuration, the dimension of its self-dual realization space, whether the realization space and the self-dual realization space coincide, whether the matroid is stable (cf. Prop. 3.1 in Self-dual matroids from canonical curves). Note that in this list only the property stability is independent of the chosen characteristic, which is set to zero for all the above mentioned properties that depend on an underlying field. Attention: We do not have a complete list of the following properties: whether a matroid is realizable by a self-dual point configuration (not known for 6 of the 1042 matroids), dimension of the self-dual realization space and whether the realization space and the self-dual realization space coincide (both not known for 288 of the 1042 matroids). Whenever the property could not be computed, the property is missing from the object.
