Kepler sets of linear recurrence sequences

D. Berend; R. Kumar

doi:10.1007/s10474-025-01506-6

Kepler sets of linear recurrence sequences

D. Berend, R. Kumar

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The Kepler set of a sequence (an)n=0∞ is the closure of the set of consecutive ratios {an+1/an:n≥0}. Following several studies, dealing with Kepler sets of recurrence sequences of order 2, we study here the case of recurrences of any order.

Original language	English
Journal	Acta Mathematica Hungarica
DOIs	https://doi.org/10.1007/s10474-025-01506-6
State	Accepted/In press - 1 Jan 2025

Keywords

Kepler set
Minkowski operation
generalized conic
linear recurrence sequence
ratio set
the Fermat–Weber location problem

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s10474-025-01506-6

Cite this

@article{7a4d6b255b0248ecaa0662dfc57c6ab5,

title = "Kepler sets of linear recurrence sequences",

abstract = "The Kepler set of a sequence (an)n=0∞ is the closure of the set of consecutive ratios {an+1/an:n≥0}. Following several studies, dealing with Kepler sets of recurrence sequences of order 2, we study here the case of recurrences of any order.",

keywords = "Kepler set, Minkowski operation, generalized conic, linear recurrence sequence, ratio set, the Fermat–Weber location problem",

author = "D. Berend and R. Kumar",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = jan,

day = "1",

doi = "10.1007/s10474-025-01506-6",

language = "English",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",

publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Kepler sets of linear recurrence sequences

AU - Berend, D.

AU - Kumar, R.

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025/1/1

Y1 - 2025/1/1

N2 - The Kepler set of a sequence (an)n=0∞ is the closure of the set of consecutive ratios {an+1/an:n≥0}. Following several studies, dealing with Kepler sets of recurrence sequences of order 2, we study here the case of recurrences of any order.

AB - The Kepler set of a sequence (an)n=0∞ is the closure of the set of consecutive ratios {an+1/an:n≥0}. Following several studies, dealing with Kepler sets of recurrence sequences of order 2, we study here the case of recurrences of any order.

KW - Kepler set

KW - Minkowski operation

KW - generalized conic

KW - linear recurrence sequence

KW - ratio set

KW - the Fermat–Weber location problem

UR - http://www.scopus.com/inward/record.url?scp=85218043428&partnerID=8YFLogxK

U2 - 10.1007/s10474-025-01506-6

DO - 10.1007/s10474-025-01506-6

M3 - Article

SN - 0236-5294

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

ER -

Kepler sets of linear recurrence sequences

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this