Combinatorics of periodic ellipsoidal billiards

George E. Andrews, Vladimir Dragović, Milena Radnović

Research output: Contribution to journalArticlepeer-review

Abstract

We study combinatorics of billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in d-dimensional Euclidean and pseudo-Euclidean spaces. Such partitions uniquely codify the sets of caustics, up to their types, which generate periodic trajectories. The period of a periodic trajectory is the largest part while the winding numbers are the remaining summands of the corresponding partition. In order to take into account the types of caustics as well, we introduce weighted partitions and provide closed forms for the generating functions of these partitions.

Original languageEnglish (US)
JournalRamanujan Journal
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Combinatorics of periodic ellipsoidal billiards'. Together they form a unique fingerprint.

Cite this