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Recursive Formula for the Random String Word Detection Probability, Overlaps and Probability Extremes

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  • V. I. Ilyevsky

Abstract

In this paper, for the first time ever, the properties of the word detection probability in a random string have been investigated. The formerly known methods led to numerical evaluation of the researched probabilities only. The present work derives the simplest algorithm for calculation of the word’s at least once detection probability in a random string. A recursive formula that considers the overlap capability has been deduced for the probability under study. This formula is being used for the proposition on comparison of the word detection probabilities in a random string for the words with different periods. The result allows determining the structure of words that have maximum and minimum detection probabilities. In particular, words having equal number of alphabetic characters have been studied. It has been established, that for the words in question detection probability is minimal for the ideally symmetrical words that have irreducible period - and maximal for the words devoid of the overlap feature. These results will be useful for molecular genetics, as well as for students studying discrete mathematics, probability theory and molecular biology.

Suggested Citation

  • V. I. Ilyevsky, 2019. "Recursive Formula for the Random String Word Detection Probability, Overlaps and Probability Extremes," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(2), pages 171-180, April.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:2:p:171
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    References listed on IDEAS

    as
    1. S. Robin & J.-J. Daudin, 2001. "Exact Distribution of the Distances between Any Occurrences of a Set of Words," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 895-905, December.
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    More about this item

    Keywords

    word occurrence; probability; combinatorics; overlaps; probability extremes;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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