Graphs and Combinatorics

, Volume 9, Issue 2–4, pp 197–200 | Cite as

On the maximum number of distinct factors of a binary string

  • Jeffrey Shallit
Graphs and Combinatoric


In this note we prove that a binary string of lengthn can have no more than\(2^{k + 1} - 1 + \left( {\mathop {n - k + 1}\limits_2 } \right)\) distinct factors, wherek is the unique integer such that 2k + k - 1 ≤ n < 2k+1 + k. Furthermore, we show that for eachn, this bound is actually achieved. The proof uses properties of the de Bruijn graph.


Hamiltonian Cycle Binary String Distinct Factor Disjoint Cycle Unique Integer 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of WaterlooOntarioCanada

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