Hi Xie, Thank you for noting this issue! Please check the newly merged changes where it has been corrected: https://github.com/sagemath/sage/pull/36962
I hadn't yet added the matroid-database package (and the AllMatroids method) back then. On Monday, January 27, 2025 at 11:28:12 AM UTC Xie wrote: > Thank you. A matroid is sparse paving if both the matroid itself and its > dual are paving. This criterion can be used to count the number of sparse > paving matroids, assuming the .is_paving() method is correct. Sparse paving > matroids have several definitions, but as far as I know, their definition > is unambiguous. > > 在2025年1月27日星期一 UTC+8 02:24:58<dim...@gmail.com> 写道： > >> On Sat, Jan 25, 2025 at 11:03 PM Xie <xiehon...@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...@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/25d2ba24-eae6-46e3-903d-bb897c478f5en%40googlegroups.com.
