Billiard partitions, Fibonacci sequences, SIP classes, and quivers

Author:

Dragović Vladimir,Stošić Marko

Abstract

Starting from billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in d 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 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.

Funder

Simons Foundation

Publisher

American Mathematical Society (AMS)

Reference15 articles.

1. Combinatorics of the periodic billiards within quadrics;Andrews, George E.;Ramanujan J.,2023

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4. Linked partition ideals and Euclidean billiard partitions;Chern, Shane;Rev. R. Acad. Cienc. Exactas F\'{\i}s. Nat. Ser. A Mat. RACSAM,2023

5. Periodic Ellipsoidal Billiard Trajectories and Extremal Polynomials;Dragović, Vladimir;Comm. Math. Phys.,2019

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