On Sat, Jan 25, 2025 at 11:03 PM Xie <xiehongyes...@gmail.com> wrote: > > for M in matroids.AllMatroids(8, type='sparse_paving'): > ....: print(M) > sparse_paving_n08_r04_#0: Matroid of rank 4 on 8 elements with 56 bases > sparse_paving_n08_r05_#0: Matroid of rank 5 on 8 elements with 48 bases > sparse_paving_n08_r06_#0: Matroid of rank 6 on 8 elements with 24 bases > sparse_paving_n08_r07_#0: Matroid of rank 7 on 8 elements with 8 bases > sparse_paving_n08_r07_#1: Matroid of rank 7 on 8 elements with 7 bases > sparse_paving_n08_r08_#0: Matroid of rank 8 on 8 elements with 1 bases > > This can't be correct because almost all matroids are sparse paving.
this has been conjectured to be held asymptotically (i.e. as # n of elements goes to infinity) in https://doi.org/10.1016/j.ejc.2011.01.016 and https://www.sciencedirect.com/science/article/pii/S0196885812000802 With this in mind, it's hard to understand what exactly could be wrong there (as this is something for n=8, not for n->oo) > > In SageMath, the is_sparse_paving‘s Docstring defines: > > *"Return if 'self' is sparse-paving. > > A matroid is sparse-paving if the symmetric difference of every pair of > circuits is greater than 2."* > > I believe this is incorrect! indeed, this seems strange, and no references are provided. I've left a comment to this effect here: https://github.com/sagemath/sage/pull/36962#issuecomment-2614537747 > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion visit > https://groups.google.com/d/msgid/sage-support/a0f42d8e-a377-465e-b224-04166d86bc80n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-support/CAAWYfq1Wk%3DjcpwE4iZo9-SUJnaXgusnpdOCtnt1QXW0UCf4Nbw%40mail.gmail.com.
