Kepler sets of linear recurrence sequences

D. Berend; R. Kumar

doi:10.1007/s10474-025-01506-6

Kepler sets of linear recurrence sequences

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
Pages (from-to)	54-95
Number of pages	42
Journal	Acta Mathematica Hungarica
Volume	175
Issue number	1
DOIs	https://doi.org/10.1007/s10474-025-01506-6
State	Published - 1 Feb 2025

Keywords

generalized conic
Kepler set
linear recurrence sequence
Minkowski operation
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{d52cabf61342466faef62eb7a969e25a,

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

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

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

year = "2025",

month = feb,

day = "1",

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

language = "English",

volume = "175",

pages = "54--95",

journal = "Acta Mathematica Hungarica",

issn = "0236-5294",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Kepler sets of linear recurrence sequences

AU - Berend, D.

AU - Kumar, R.

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

PY - 2025/2/1

Y1 - 2025/2/1

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 - generalized conic

KW - Kepler set

KW - linear recurrence sequence

KW - Minkowski operation

KW - ratio set

KW - the Fermat–Weber location problem

UR - http://www.scopus.com/inward/record.url?scp=105001088332&partnerID=8YFLogxK

U2 - 10.1007/s10474-025-01506-6

DO - 10.1007/s10474-025-01506-6

M3 - Article

AN - SCOPUS:105001088332

SN - 0236-5294

VL - 175

SP - 54

EP - 95

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1

ER -

Kepler sets of linear recurrence sequences

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this