We give a one-step construction of de Bruijn sequences of general alphabet size and with
order n+ k n+ k, given a de Bruijn sequence of order n and any integer k> 1 k> 1. This is …

This paper presents a method to find new de Bruijn sequences based on ones of lesser
order. This is done by mapping a de Bruijn cycle to several vertex disjoint cycles in a de …

A de Bruijn sequence of order n over a k-symbol alphabet is a circular sequence where
each length-n sequence occurs exactly once. We present a way of extending de Bruijn …

We give a complete proof of the following theorem: 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 …

We generalize the notion of a de Bruijn sequence to a" multi de Bruijn sequence": a cyclic or
linear sequence that contains every k-mer over an alphabet of size q exactly m times. For …

A (non-circular) de Bruijn sequence w of order n is a word such that every word of length n
appears exactly once in w as a factor. In this paper, we generalize the concept to different …

Pick any length n binary string b 1 b 2⋯ bn and remove the first bit b 1. If b 2 b 3⋯ bn 1 is a
necklace, then append the complement of b 1 to the end of the remaining string; otherwise …

We study graph homomorphisms from a de Bruijn digraph of higher order to one of lower
order. A main theme of this thesis is to characterize de Bruijn graph homomorphisms such …

We present an algorithm for the generation of m-ary de Bruijn cycles. The algorithm
generates m kg (n, k) cycles of length mn, using 3n+ kg (n, k) storage, where k is a free …

A k-ary de Bruijn sequence of order n is a cyclic sequence of length kn in which each k-ary
string of length n appears exactly once as a substring. A shift rule for a de Bruijn sequence of …