Accurate Prediction of the Statistics of Repetitions in Random Sequences: A Case Study in Archaea Genomes

Repetitive patterns in genomic sequences have a great biological significance and also algorithmic implications. Analytic combinatorics allow to derive formula for the expected length of repetitions in a random sequence. Asymptotic results, that generalize previous works on a binary alphabet, are easily computable. Simulations on random sequences show their accuracy. As an application, the sample case of Archaea genomes illustrates how biological sequences may differ from random sequences.