PD Dr. Andreas Paffenholz

Lists of Combinatorial Types of Birkhoff Faces

The following lists contain a description of all combinatorial types of faces of some Birkhoff polytope of the given dimension. The files are split into dimension and product/non-product types. Each file contains an array of a pairs of a graph and an incidence matrix.

The lists are in the polymake format. Note that you need a perpetual beta release to read the files.

Please contact me if you have any questions about these lists or faces of Birkoff polytopes. If you find these lists useful for your research then I would like to hear about how you used them.

Type Number of Types File
1-dimensional non-product types 1 birkhoff.1D.faces.pdata
2-dimensional non-product types 1 birkhoff.2D.faces.pdata
2-dimensional product types 1 birkhoff.2D.product.faces.pdata
3-dimensional non-product types 2 birkhoff.3D.faces.pdata
3-dimensional product types 3 birkhoff.3D.product.faces.pdata
4-dimensional non-product types 6 birkhoff.4D.faces.pdata
4-dimensional product types 5 birkhoff.4D.product.faces.pdata
5-dimensional non-product types 20 birkhoff.5D.faces.pdata
5-dimensional product types 13 birkhoff.5D.product.faces.pdata
6-dimensional non-product types 86 birkhoff.6D.faces.pdata
6-dimensional product types 43 birkhoff.6D.product.faces.pdata
7-dimensional non-product types 498 birkhoff.7D.faces.pdata
7-dimensional product types 163 birkhoff.7D.product.faces.pdata
8-dimensional non-product types 3712 birkhoff.8D.faces.pdata
8-dimensional product types 818 birkhoff.8D.product.faces.pdata