English

The Discrepancy of the Lex-Least De Bruijn Sequence

Combinatorics 2009-03-24 v1

Abstract

We answer the following question of R. L. Graham: What is the discrepancy of the lexicographically-least binary de Bruijn sequence? Here, "discrepancy" refers to the maximum (absolute) difference between the number of ones and the number of zeros in any initial segment of the sequence. We show that the answer is Θ(2nlogn/n)\Theta(2^n \log n/n).

Cite

@article{arxiv.0903.3753,
  title  = {The Discrepancy of the Lex-Least De Bruijn Sequence},
  author = {Joshua Cooper and Christine Heitsch},
  journal= {arXiv preprint arXiv:0903.3753},
  year   = {2009}
}

Comments

11 pages, 0 figures

R2 v1 2026-06-21T12:43:09.047Z