تقرير
Polynomials from combinatorial $K$-theory
| العنوان: | Polynomials from combinatorial $K$-theory |
|---|---|
| المؤلفون: | Monical, Cara, Pechenik, Oliver, Searles, Dominic |
| المصدر: | Can. J. Math.-J. Can. Math. 73 (2021) 29-62 |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05E05 |
| الوصف: | We introduce two new bases of the ring of polynomials and study their relations to known bases. The first basis is the quasiLascoux basis, which is simultaneously both a $K$-theoretic deformation of the quasikey basis and also a lift of the $K$-analogue of the quasiSchur basis from quasisymmetric polynomials to general polynomials. We give positive expansions of this quasiLascoux basis into the glide and Lascoux atom bases, as well as a positive expansion of the Lascoux basis into the quasiLascoux basis. As a special case, these expansions give the first proof that the $K$-analogues of quasiSchur polynomials expand positively in multifundamental quasisymmetric polynomials of T. Lam and P. Pylyavskyy. The second new basis is the kaon basis, a $K$-theoretic deformation of the fundamental particle basis. We give positive expansions of the glide and Lascoux atom bases into this kaon basis. Throughout, we explore how the relationships among these $K$-analogues mirror the relationships among their cohomological counterparts. We make several 'alternating sum' conjectures that are suggestive of Euler characteristic calculations. Comment: 35 pages, 10 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.4153/S0008414X19000464 |
| URL الوصول: | http://arxiv.org/abs/1806.03802 |
| رقم الأكسشن: | edsarx.1806.03802 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.4153/S0008414X19000464 |
|---|