Concrete Math
On a Conjecture by Eriksson Concerning Overlap in Strings
Combinatorics, Probability and Computing
Fast and Sensitive Probe Selection for DNA Chips Using Jumps in Matching Statistics
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
Combinatorics of periods in strings
Journal of Combinatorial Theory Series A
Efficient computation of shortest absent words in a genomic sequence
Information Processing Letters
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Determining the distribution of the number of empty urns after a number of balls have been thrown randomly into the urns is a classical and well understood problem. We study a generalization: Given a finite alphabet of size σ and a word length q, what is the distribution of the number X of words (of length q) that do not occur in a random text of length n+q−1 over the given alphabet? For q=1, X is the number Y of empty urns with σ urns and n balls. For q⩾2, X is related to the number Y of empty urns with σq urns and n balls, but the law of X is more complicated because successive words in the text overlap. We show that, perhaps surprisingly, the laws of X and Y are not as different as one might expect, but some problems remain currently open.