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Annual Symposium on Combinatorial Pattern Matching

CPM 1999: Combinatorial Pattern Matching pp 115–122Cite as

Bounds on the Number of String Subsequences

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1645))

Abstract

The problem considered is that of determining the number of subsequences obtainable by deleting t symbols from a string of length n over an alphabet of size s. Recurrences are proven and solved for the maximum and average case values, and bounds on these values are exhibited.

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References

  1. L. Calabi, “On the computation of Levenshtein’s distances,” TM-9-0030, Parke Math. Labs., Inc., Carlisle, Mass., 1967.

    Google Scholar 

  2. L. Calabi and W.E. Hartnett, “Some general results of coding theory with applications to the study of codes for the correction of synchronization errors,” Information and Control 15,3 (Sept 1969) 235–249. Reprinted in: W.E. Hartnett (ed), Foundations of Coding Theory (1974) Chapter 7, pp.107-121.

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  3. V.I. Levenshtein, “Binary codes capable of correcting deletions, insertions and reversals,” Soviet Phys. Dokl. 10 (1966) 707–710.

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  4. V.I. Levenshtein, “Elements of the coding theory,” in: Discrete Math. and Math. Probl. of Cybern., Nauka, Moscow (1974) 207–235 (in Russian).

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  5. V.I. Levenshtein, “On perfect codes in deletion and insertion metric,” Discrete Math. Appl. 2,3 (1992) 241–258. Originally published in Diskretnaya Matematika 3,1 (1991) 3-20 (in Russian).

    Article  Google Scholar 

  6. V.I. Levenshtein, “Reconstructing binary sequences by the minimum number of their subsequences or supersequences of a given length,” Proc. 5th Int. Wkshp on Alg. & Comb. Coding Theory, Sozopol, Bulgaria (1996) 176–183.

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  7. C.L. Liu, Introduction to Combinatorial Mathematics, McGraw-Hill, 1986, pp. 80–86.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information and Computer Science, University of California at Irvine, Irvine, CA, 92697-3425, USA

    Daniel S. Hirschberg

Authors
  1. Daniel S. Hirschberg
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Editor information

Editors and Affiliations

  1. Institute Gaspard-Monge, University of Marne-la-Vallée, F 77454, Marne-la-Vallée Cedex 2, France

    Maxime Crochemore

  2. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, England

    Mike Paterson

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© 1999 Springer-Verlag Berlin Heidelberg

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Hirschberg, D.S. (1999). Bounds on the Number of String Subsequences. In: Crochemore, M., Paterson, M. (eds) Combinatorial Pattern Matching. CPM 1999. Lecture Notes in Computer Science, vol 1645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48452-3_9

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  • DOI: https://doi.org/10.1007/3-540-48452-3_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66278-5

  • Online ISBN: 978-3-540-48452-3

  • eBook Packages: Springer Book Archive

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