تقرير
Ternary and quaternary positroids
| العنوان: | Ternary and quaternary positroids |
|---|---|
| المؤلفون: | Quail, Jeremy |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05B35 |
| الوصف: | A positroid is an ordered matroid realizable by a real matrix with all nonnegative maximal minors. Postnikov gave a map from ordered matroids to Grassmann necklaces, for which there is a unique positroid in each fiber of the map. Here, we give forbidden minor characterizations of ternary and quaternary positroids. We show that a positroid is ternary if and only if it is near-regular, and that all ternary positroids are formed by direct sums and $2$-sums of binary positroids and positroid ordered whirls. We prove that a positroid is quaternary if and only if it is $U^2_6, U^4_6,$ and $P_6$-free. Under the map from ordered matroids to Grassmann necklaces, we fully characterize the fibers of ternary positroids, referred to as their positroid envelope classes; in particular, the envelope class of a positroid ordered whirl of rank-$r$ contains exactly four matroids. Comment: arXiv admin note: text overlap with arXiv:2402.17841 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.06956 |
| رقم الأكسشن: | edsarx.2403.06956 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |