Authors: Andrews, George E.
Dragović, Vladimir 
Radnović, Milena
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Combinatorics of periodic ellipsoidal billiards
Journal: Ramanujan Journal
Issue Date: 2021
Rank: ~M21
ISSN: 1382-4090
DOI: 10.1007/s11139-020-00346-y
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.
Keywords: Euclidean billiard partitions | Generating functions | Irreducible partitions | Light-type partitions | Space-type partitions | Time-type partitions | Weighted Euclidean billiard partitions
Publisher: Springer Link

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