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 |