The k-nacci sequences in some special modular groups

Omur Deveci; Colin Matthew Campbell

doi:10.1142/S1005386714000042

The k-nacci sequences in some special modular groups

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Abstract

A k-nacci (k-step Fibonacci) sequence in a finite group is a sequence of group elements x_{0, x_{1, x₂, …, x_n, … for which, given an initial (seed) set x₀, x₁, x₂, …, x_j-1, each element is defined by}

From the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x₀, x₁, x₂, …, x_j-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups 픐₂, and ℜ₂, where each term of the sequence is reduced modulo 2.}

Original language	English
Pages (from-to)	17-30
Journal	Algebra Colloquium
Volume	21
Issue number	59
DOIs	https://doi.org/10.1142/S1005386714000042
Publication status	Published - 2014

Keywords

k-nacci sequence
period
modular group

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10.1142/S1005386714000042

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title = "The k-nacci sequences in some special modular groups",

abstract = " A k-nacci (k-step Fibonacci) sequence in a finite group is a sequence of group elements x0, x1, x2, …, xn, … for which, given an initial (seed) set x0, x1, x2, …, xj-1, each element is defined by From the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x0, x1, x2, …, xj-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups 픐2, and ℜ2, where each term of the sequence is reduced modulo 2. ",

keywords = "k-nacci sequence, period, modular group",

author = "Omur Deveci and Campbell, {Colin Matthew}",

year = "2014",

doi = "10.1142/S1005386714000042",

language = "English",

volume = "21",

pages = "17--30",

journal = "Algebra Colloquium",

issn = "1005-3867",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "59",

}

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T1 - The k-nacci sequences in some special modular groups

AU - Deveci, Omur

AU - Campbell, Colin Matthew

PY - 2014

Y1 - 2014

N2 - A k-nacci (k-step Fibonacci) sequence in a finite group is a sequence of group elements x0, x1, x2, …, xn, … for which, given an initial (seed) set x0, x1, x2, …, xj-1, each element is defined by From the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x0, x1, x2, …, xj-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups 픐2, and ℜ2, where each term of the sequence is reduced modulo 2.

AB - A k-nacci (k-step Fibonacci) sequence in a finite group is a sequence of group elements x0, x1, x2, …, xn, … for which, given an initial (seed) set x0, x1, x2, …, xj-1, each element is defined by From the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x0, x1, x2, …, xj-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups 픐2, and ℜ2, where each term of the sequence is reduced modulo 2.

KW - k-nacci sequence

KW - period

KW - modular group

U2 - 10.1142/S1005386714000042

DO - 10.1142/S1005386714000042

M3 - Article

SN - 1005-3867

VL - 21

SP - 17

EP - 30

JO - Algebra Colloquium

JF - Algebra Colloquium

IS - 59

ER -

The k-nacci sequences in some special modular groups

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Keywords

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