Artículo
Perfect necklaces
Alvarez, Nicolás Alejandro
; Becher, Veronica Andrea
; Ferrari, Pablo Augusto
; Yuhjtman, Sergio Andrés
Fecha de publicación:
09/2016
Editorial:
Academic Press Inc Elsevier Science
Revista:
Advances In Applied Mathematics
ISSN:
0196-8858
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We introduce a variant of de Bruijn words that we call perfect necklaces. Fix a finite alphabet. Recall that a word is a finite sequence of symbols in the alphabet and a circular word, or necklace, is the equivalence class of a word under rotations. For positive integers k and n, we call a necklace (k,n)-perfect if each word of length k occurs exactly n times at positions which are different modulo n for any convention on the starting point. We call a necklace perfect if it is (k,k)-perfect for some k. We prove that every arithmetic sequence with difference coprime with the alphabet size induces a perfect necklace. In particular, the concatenation of all words of the same length in lexicographic order yields a perfect necklace. For each k and n, we give a closed formula for the number of (k,n)-perfect necklaces. Finally, we prove that every infinite periodic sequence whose period coincides with some (k,n)-perfect necklace for some k and some n, passes all statistical tests of size up to k, but not all larger tests. This last theorem motivated this work.
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Articulos (ICIC)
Articulos de INSTITUTO DE CS. E INGENIERIA DE LA COMPUTACION
Articulos de INSTITUTO DE CS. E INGENIERIA DE LA COMPUTACION
Articulos(CCT - BAHIA BLANCA)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - BAHIA BLANCA
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - BAHIA BLANCA
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Articulos de INSTITUTO DE INVESTIGACION EN CIENCIAS DE LA COMPUTACION
Articulos de INSTITUTO DE INVESTIGACION EN CIENCIAS DE LA COMPUTACION
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Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Alvarez, Nicolás Alejandro; Becher, Veronica Andrea; Ferrari, Pablo Augusto; Yuhjtman, Sergio Andrés; Perfect necklaces; Academic Press Inc Elsevier Science; Advances In Applied Mathematics; 80; 9-2016; 48-61
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