IJPAM: Volume 76, No. 3 (2012)

A NECESSARY AND SUFFICIENT CONDITION FOR A SET
OF SEQUENCES ON THE GENETIC ALPHABET
TO BE A CIRCULAR CODE

Giuseppe Pirillo
Consiglio Nazionale delle Ricerche
Dipartimento di Matematica ``U.Dini"
Università di Firenze
viale Morgagni 67/A, 50134, Firenze, ITALIA
and
Université de Marne-la-Vallée
5, Boulevard Descartes
Champs sur Marne
77454, Marne-la-Vallée Cedex 2, FRANCE


Abstract. The maximal circular code discovered by Arquès and Michel contains 20 trinucleotides, i.e. sequences of length three on the genetic alphabet. Necessary and sufficient conditions for a set of trinucleotides to be a circular code was stated and proved in a previous paper. Here we present an analogous result for sets of sequences of length four on the genetic alphabet. More precisely we prove that these sets are circular codes if and only if they have no unbalanced 5-necklaces and no balanced 9-necklaces.

Received: February 10, 2012

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 3