* https://github.com/sagemath/sage/pull/39382
On Tuesday, February 11, 2025 at 2:06:03 PM UTC gmou3 wrote: > 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/96201f93-9925-4188-80d1-8bf8291f0632n%40googlegroups.com.
