Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2404.19078 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929331552387072 |
|---|---|
| author | Dragović, Vladimir Stošić, Marko |
| author_facet | Dragović, Vladimir Stošić, Marko |
| contents | Starting from billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in $d$-dimensional Euclidean space, we introduce a new type of separable integer partition classes, called type B. We study the numbers of basis partitions with $d$ parts and relate them to the Fibonacci sequence and its natural generalizations. Remarkably, the generating series of basis partitions can be related to the quiver generating series of symmetric quivers corresponding to the framed unknot via knots-quivers correspondence, and to the count of Schröder paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Billiard Partitions, Fibonacci Sequences, SIP Classes, and Quivers Dragović, Vladimir Stošić, Marko Combinatorics High Energy Physics - Theory Mathematical Physics Dynamical Systems Quantum Algebra 05A15, 05A17, 14H70, 37J35, 16G20, 26C05 Starting from billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in $d$-dimensional Euclidean space, we introduce a new type of separable integer partition classes, called type B. We study the numbers of basis partitions with $d$ parts and relate them to the Fibonacci sequence and its natural generalizations. Remarkably, the generating series of basis partitions can be related to the quiver generating series of symmetric quivers corresponding to the framed unknot via knots-quivers correspondence, and to the count of Schröder paths. |
| title | Billiard Partitions, Fibonacci Sequences, SIP Classes, and Quivers |
| topic | Combinatorics High Energy Physics - Theory Mathematical Physics Dynamical Systems Quantum Algebra 05A15, 05A17, 14H70, 37J35, 16G20, 26C05 |
| url | https://arxiv.org/abs/2404.19078 |