تقرير
Quotients of M-convex sets and M-convex functions
| العنوان: | Quotients of M-convex sets and M-convex functions |
|---|---|
| المؤلفون: | Brandenburg, Marie-Charlotte, Loho, Georg, Smith, Ben |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Mathematics - Algebraic Geometry, Mathematics - Optimization and Control, 05B35, 14T15, 52B20, 52B40 (Primary) 14M15, 90C25, 90C27 (Secondary) |
| الوصف: | We unify the study of quotients of matroids, polymatroids, valuated matroids and strong maps of submodular functions in the framework of Murota's discrete convex analysis. As a main result, we compile a list of ten equivalent characterizations of quotients for M-convex sets, generalizing existing formulations for (poly)matroids and submodular functions. We also initiate the study of quotients of M-convex functions, constructing a hierarchy of four separate characterizations. Our investigations yield new insights into the fundamental operation of induction, as well as the structure of linking sets and linking functions, which are generalizations of linking systems and bimatroids. Comment: 44 pages, 2 figures. Comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.07751 |
| رقم الأكسشن: | edsarx.2403.07751 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |