TY - UNPB

T1 - On Embedding De Bruijn Sequences by Increasing the Alphabet Size.

AU - Schwartz, Moshe

AU - Svoray, Yotam

AU - Weiss, Gera

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2019

Y1 - 2019

N2 - The generalization of De Bruijn sequences to infinite sequences with respect to the order n has been studied iand it was shown that every de Bruijn sequence of order n in at least three symbols can be extended to a de Bruijn sequence of order n+1. Every de Bruijn sequence of order n in two symbols can not be extended to order n+1, but it can be extended to order n+2. A natural question to ask is if this theorem is true with respect to the alphabet. That is, we would like to understand if we can extend a De Bruijn sequence of order n over alphabet k into a into a De Bruijn sequence of order n and alphabet k+1. We call a De Bruijn sequence with this property an Onion De Bruijn sequence. In this paper we show that the answer to this question is positive. In fact, we prove that the well known Prefer Max De Bruijn sequence has this property, and in fact every sequence with this property behaves like the Prefer max De Bruijn sequence.

AB - The generalization of De Bruijn sequences to infinite sequences with respect to the order n has been studied iand it was shown that every de Bruijn sequence of order n in at least three symbols can be extended to a de Bruijn sequence of order n+1. Every de Bruijn sequence of order n in two symbols can not be extended to order n+1, but it can be extended to order n+2. A natural question to ask is if this theorem is true with respect to the alphabet. That is, we would like to understand if we can extend a De Bruijn sequence of order n over alphabet k into a into a De Bruijn sequence of order n and alphabet k+1. We call a De Bruijn sequence with this property an Onion De Bruijn sequence. In this paper we show that the answer to this question is positive. In fact, we prove that the well known Prefer Max De Bruijn sequence has this property, and in fact every sequence with this property behaves like the Prefer max De Bruijn sequence.

U2 - https://doi.org/10.48550/arXiv.1906.06157

DO - https://doi.org/10.48550/arXiv.1906.06157

M3 - Preprint

BT - On Embedding De Bruijn Sequences by Increasing the Alphabet Size.

ER -