The number of runs in a string
Information and Computation
Maximal repetitions in strings
Journal of Computer and System Sciences
How many runs can a string contain?
Theoretical Computer Science
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Theoretical Computer Science
On the maximal sum of exponents of runs in a string
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Hunting redundancies in strings
DLT'11 Proceedings of the 15th international conference on Developments in language theory
On the structure of run-maximal strings
Journal of Discrete Algorithms
The three squares lemma revisited
Journal of Discrete Algorithms
On the maximal number of cubic runs in a string
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
The maximal number of cubic runs in a word
Journal of Computer and System Sciences
On the maximum number of cubic subwords in a word
European Journal of Combinatorics
Computing regularities in strings: A survey
European Journal of Combinatorics
Computing maximum number of runs in strings
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
| Hi-index | 0.00 |
Since the work of Kolpakov and Kucherov in [5,6], it is known that ρ(n), the maximal number of runs in a string, is linear in the length nof the string. A lower bound of $3/(1 + \sqrt{5})n \sim 0.927n$ has been given by Franek and al. [3,4], and upper bounds have been recently provided by Rytter, Puglisi and al., and Crochemore and Ilie (1.6n) [8.7.1]. However, very few properties are known for the ρ(n)/nfunction. We show here by a simple argument that limn→ ∞ρ(n)/nexists and that this limit is never reached. Moreover, we further study the asymptotic behavior of ρp(n), the maximal number of runs with period at most p. We provide a new bound for some microruns : we show that there is no more than 0.971 nruns of period at most 9 in binary strings. Finally, this technique improves the previous best known upper bound, showing that the total number of runs in a binary string of length nis below 1.52n.