Matroids with 9 elements

<p>This dataset contains the&nbsp;385370 pairwise non-isomorphic&nbsp;matroids from 0 to 9 elements inclusive.</p> <p>Each matroid is given as a text string occupying one line of the file matroids09_rankLine. Except for&nbsp;the empty matroid, the text string gives the rank of every subset of the groundset (as described&nbsp;in more detail in the readme.md file), and so is called the rankline of the matroid.</p> <p>This establishes a de-facto&nbsp;numbering scheme for the matroids,&nbsp;starting with&nbsp;M0 (the empty matroid) and ending with&nbsp;M385369 (the uniform matroid U(9,9)). For example, M298 is the number for the Fano plane, and its rankLine&nbsp;occurs on line 298 (counting from 0) of the file.</p> <p>Various published papers in matroid theory&nbsp;have already referred to specific matroids using the M-numbers obtained from this catalogue.</p> <p>This dataset is provided as a &quot;reference version&quot; of the catalogue to permit researchers, both now and into the future, to safely use M-numbers as unique and unchanging identifiers to refer to&nbsp;any matroid on up to 9 elements.</p>