تقرير
A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials
| العنوان: | A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials |
|---|---|
| المؤلفون: | Tom, Foster |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Primary 05E05, Secondary 05E10, 05C15 |
| الوصف: | In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of the horizontal-strip LLT polynomial $G_\lambda(x;q)$ in some special cases. We associate a weighted graph $\Pi$ to $\lambda$ and we use it to express a linear relation among LLT polynomials. We apply this relation to prove an explicit combinatorial Schur-positive expansion of $G_\lambda(x;q)$ whenever $\Pi$ is triangle-free. We also prove that the largest power of $q$ in the LLT polynomial is the total edge weight of our graph. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2011.13671 |
| رقم الأكسشن: | edsarx.2011.13671 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |