DeepAI AI Chat
Log In Sign Up

On Embedding De Bruijn Sequences by Increasing the Alphabet Size

by   Moshe Schwartz, et al.

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.


page 1

page 2

page 3

page 4


Extending de Bruijn sequences to larger alphabets

A circular de Bruijn sequence of order n in an alphabet of k symbols is ...

A construction of a λ- Poisson generic sequence

Years ago Zeev Rudnick defined the λ-Poisson generic sequences as the in...

A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

We propose a novel construction for the well-known prefer-max De Bruijn ...

Almost Every Simply Typed Lambda-Term Has a Long Beta-Reduction Sequence

It is well known that the length of a beta-reduction sequence of a simpl...

On Layer-Rainbow Latin Cubes Containing Layer-Rainbow Latin Cubes

Despite the fact that latin cubes have been studied since in the 1940's,...

Improving Order with Queues

Patience Sort sorts a sequence of numbers with a minimal number of queue...

An Information-Theoretical Analysis of the Minimum Cost to Erase Information

We normally hold a lot of confidential information in hard disk drives a...