تقرير
Combinatorial Derived Matroids
| العنوان: | Combinatorial Derived Matroids |
|---|---|
| المؤلفون: | Kuznetsova, Olga, Freij-Hollanti, Ragnar, Jurrius, Relinde |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | Let $M$ be an arbitrary matroid with circuits $\mathcal{C}(M)$. We propose a definition of a derived matroid $\delta M$ that has as its ground set $\mathcal{C}(M)$. Unlike previous attempts of such a definition, our definition applies to arbitrary matroids, and is completely combinatorial. We prove that the rank of $\delta M$ is bounded from above by $|M|-r(M)$, that it is connected if and only if $M$ is connected. We compute examples including the derived matroids of uniform matroids, the V\'amos matroid and the graphical matroid $M(K_4)$. We formulate conjectures relating our construction to previous definitions of derived matroids. Comment: Errors in Section 6 of a previous version corrected |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2206.06881 |
| رقم الأكسشن: | edsarx.2206.06881 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |