تقرير
Chromatic symmetric functions and change of basis
| العنوان: | Chromatic symmetric functions and change of basis |
|---|---|
| المؤلفون: | Sagan, Bruce E., Tom, Foster |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Primary 05E05, Secondary 05C15, 05C31, 05E10 |
| الوصف: | We prove necessary conditions for certain elementary symmetric functions, $e_\lambda$, to appear with nonzero coefficient in Stanley's chromatic symmetric function as well as in the generalization considered by Shareshian and Wachs. We do this by first considering the expansion in the monomial or Schur basis and then performing a basis change. Using the former, we make a connection with two fundamental graph theory invariants, the independence and clique numbers. This allows us to prove nonnegativity of three-column coefficients for all natural unit interval graphs. The Schur basis permits us to give a new interpretation of the coefficient of $e_n$ in terms of tableaux. We are also able to give an explicit formula for that coefficient. Comment: 21 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.06155 |
| رقم الأكسشن: | edsarx.2407.06155 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |