تقرير
A Proof of the Strict Monotone 5-step Conjecture
| العنوان: | A Proof of the Strict Monotone 5-step Conjecture |
|---|---|
| المؤلفون: | Gallagher, J. Mackenzie, Morris, Jr, Walter D. |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 52B05 |
| الوصف: | A computer search through the oriented matroid programs with dimension 5 and 10 facets shows that the maximum strictly monotone diameter is 5. Thus $\Delta_{sm}(5,10)=5$. This enumeration is analogous to that of Bremner and Schewe for the non-monotone diameter of 6-polytopes with 12 facets. Similar enumerations show that $\Delta_{sm}(4,9)=5$ and $\Delta_m(4,9)=\Delta_m(5,10)=6.$ We shorten the known non-computer proof of the strict monotone 4-step conjecture. Comment: In Sections 2 and 3, "n-d" and "d" had been switched |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1806.03403 |
| رقم الأكسشن: | edsarx.1806.03403 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |