# A necklace algorithm to determine the growth function of trinucleotide circular codes

Matthieu Luc Herrmann, Christian Michel, Benoît Sugmeyer

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

Circular codes are mathematical objects studied in combinatorics - theoretical computer science, and theoretical biology. So far, there is no close formulas allowing to determine the growth function (number and list) of circular codes. This combinatorial problem can only be solved by an algorithmic approach. We propose a new algorithm based on a necklace proposition to determine the growth function of trinucleotide circular codes, a trinucleotide being a word of 3 letters on a 4-letter alphabet. This necklace algorithm, unique in its class, can be extended in future to the analysis of codes, e.g. circular codes, containing words greater than 3 letters and also over larger alphabets.
Original language English 1-40 Journal of Applied Mathematics & Bioinformatics Published - 2013 Yes

### Keywords

• Circular code
• Genetic code
• necklace algorithm
• combinatorial algorithm

### Cite this

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title = "A necklace algorithm to determine the growth function of trinucleotide circular codes",
abstract = "Circular codes are mathematical objects studied in combinatorics - theoretical computer science, and theoretical biology. So far, there is no close formulas allowing to determine the growth function (number and list) of circular codes. This combinatorial problem can only be solved by an algorithmic approach. We propose a new algorithm based on a necklace proposition to determine the growth function of trinucleotide circular codes, a trinucleotide being a word of 3 letters on a 4-letter alphabet. This necklace algorithm, unique in its class, can be extended in future to the analysis of codes, e.g. circular codes, containing words greater than 3 letters and also over larger alphabets.",
keywords = "Circular code, Genetic code, necklace algorithm, combinatorial algorithm",
author = "Herrmann, {Matthieu Luc} and Christian Michel and Beno{\^i}t Sugmeyer",
year = "2013",
language = "English",
pages = "1--40",
journal = "Journal of Applied Mathematics & Bioinformatics",
issn = "1792-6939",
publisher = "Scienpress",

}

A necklace algorithm to determine the growth function of trinucleotide circular codes. / Herrmann, Matthieu Luc; Michel, Christian; Sugmeyer, Benoît.

In: Journal of Applied Mathematics & Bioinformatics, 2013, p. 1-40.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - A necklace algorithm to determine the growth function of trinucleotide circular codes

AU - Herrmann, Matthieu Luc

AU - Michel, Christian

AU - Sugmeyer, Benoît

PY - 2013

Y1 - 2013

N2 - Circular codes are mathematical objects studied in combinatorics - theoretical computer science, and theoretical biology. So far, there is no close formulas allowing to determine the growth function (number and list) of circular codes. This combinatorial problem can only be solved by an algorithmic approach. We propose a new algorithm based on a necklace proposition to determine the growth function of trinucleotide circular codes, a trinucleotide being a word of 3 letters on a 4-letter alphabet. This necklace algorithm, unique in its class, can be extended in future to the analysis of codes, e.g. circular codes, containing words greater than 3 letters and also over larger alphabets.

AB - Circular codes are mathematical objects studied in combinatorics - theoretical computer science, and theoretical biology. So far, there is no close formulas allowing to determine the growth function (number and list) of circular codes. This combinatorial problem can only be solved by an algorithmic approach. We propose a new algorithm based on a necklace proposition to determine the growth function of trinucleotide circular codes, a trinucleotide being a word of 3 letters on a 4-letter alphabet. This necklace algorithm, unique in its class, can be extended in future to the analysis of codes, e.g. circular codes, containing words greater than 3 letters and also over larger alphabets.

KW - Circular code

KW - Genetic code

KW - necklace algorithm

KW - combinatorial algorithm

M3 - Article

SP - 1

EP - 40

JO - Journal of Applied Mathematics & Bioinformatics

JF - Journal of Applied Mathematics & Bioinformatics

SN - 1792-6939

ER -