Report
Torus knots and generalized Schr\'oder paths
| العنوان: | Torus knots and generalized Schr\'oder paths |
|---|---|
| المؤلفون: | Stošić, Marko, Sułkowski, Piotr |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematics - Combinatorics, Mathematics - Quantum Algebra |
| الوصف: | We relate invariants of torus knots to the counts of a class of lattice paths, which we call generalized Schr\"oder paths. We determine generating functions of such paths, located in a region determined by a type of a torus knot under consideration, and show that they encode colored HOMFLY-PT polynomials of this knot. The generators of uncolored HOMFLY-PT homology correspond to a basic set of such paths. Invoking the knots-quivers correspondence, we express generating functions of such paths as quiver generating series, and also relate them to quadruply-graded knot homology. Furthermore, we determine corresponding A-polynomials, which provide algebraic equations and recursion relations for generating functions of generalized Schr\"oder paths. The lattice paths of our interest explicitly enumerate BPS states associated to knots via brane constructions. Comment: 33 pages, 7 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.10161 |
| رقم الانضمام: | edsarx.2405.10161 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |