تقرير
Necessary conditions for Schur-maximality
| العنوان: | Necessary conditions for Schur-maximality |
|---|---|
| المؤلفون: | Tom, Foster, van Willigenburg, Stephanie |
| المصدر: | Electron. J. Combin. 25 50pp (2018) |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05E05 (Primary), 05E10, 06A05, 06A06, 20C30 (Secondary) |
| الوصف: | McNamara and Pylyavskyy conjectured precisely which connected skew shapes are maximal in the Schur-positivity order, which says that $B\leq _s A$ if $s_A-s_B$ is Schur-positive. Towards this, McNamara and van Willigenburg proved that it suffices to study equitable ribbons, namely ribbons whose row lengths are all of length $a$ or $(a+1)$ for $a\geq 2$. In this paper we confirm the conjecture of McNamara and Pylyavskyy in all cases where the comparable equitable ribbons form a chain. We also confirm a conjecture of McNamara and van Willigenburg regarding which equitable ribbons in general are minimal. Additionally, we establish two sufficient conditions for the difference of two ribbons to be Schur-positive, which manifest as diagrammatic operations on ribbons. We also deduce two necessary conditions for the difference of two equitable ribbons to be Schur-positive that rely on rows of length $a$ being at the end, or on rows of length $(a+1)$ being evenly distributed. Comment: 47 pages; final version to appear in Electron. J. Combin |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1711.10000 |
| رقم الأكسشن: | edsarx.1711.10000 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |