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Combinatorial analysis

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Combinatorial Computational Biology of RNA
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Abstract

In this chapter we develop the theory of k-noncrossing and k-noncrossing, σ-canonical structures. We derive their generating functions and obtain their singularity analysis, which produces simple, asymptotic formulas for the numbers of various types of k-noncrossing s-canonical structures.

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References

  1. M. Ajtai, J. Komlós, and E. Szemerédi. Largest random component of a k-cube. Combinatorica, 2:1–7, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Akutsu. Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots. Discr. Appl. Math., 104:45–62, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. Aldous and P. Diaconis. Strong uniform times and finite random walks. Adv. Appl. Math., 2:69–97, 1987.

    Article  MathSciNet  Google Scholar 

  4. P. Flajolet and R. Sedgewick. Analytic Combinatorics. Cambridge University Press, Cambridge, England, 2009.

    Google Scholar 

  5. H.S.W. Han and C.M. Reidys. Pseudoknot RNA structures with arc-length \(\ge 4\). J. Comp. bio., 9(15):1195–1208, 2008.

    Article  MathSciNet  Google Scholar 

  6. I.L. Hofacker, P. Schuster, and P.F. Stadler. Combinatorics of RNA secondary structures. Discr. Appl. Math., 88:207–237, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  7. E.Y. Jin, J. Qin, and C.M. Reidys. Combinatorics of RNA structures with pseudoknots. Bull. Math. Biol., 70:45–67, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  8. E.Y. Jin and C.M. Reidys. Asymptotic enumeration of RNA structures with pseudoknots. Bull. Math. Biol., 70:951–970, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  9. E.Y. Jin and C.M. Reidys. Combinatorial design of pseudoknot RNA. Adv. Appl. Math., 42:135–151, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  10. E.Y. Jin and C.M. Reidys. RNA pseudoknots structures with arc length-length \(\ge 3\) and stack-length-length \(\ge \sigma\). Discr. Appl. Math., 158:25–36, 2010.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Ma and C.M. Reidys. Canonical RNA pseudoknot structures. J. Comput. Biol., 15:1257–1273, 2008.

    Article  MathSciNet  Google Scholar 

  12. M. E. Nebel. Combinatorial properties of RNA secondary structures. J. Comp. Biol., 9(3):541–574, 2003.

    Article  Google Scholar 

  13. M.E. Nebel, C.M. Reidys, and R.R. Wang. Loops in canonical RNA pseudoknot structures. arXiv:0912.0429, 2009.

    Google Scholar 

  14. C.M. Reidys and R.R. Wang. Shapes of RNA pseudoknot structures. J. Comp. Biol., 2009. to appear.

    Google Scholar 

  15. W.R. Schmitt and M.S. Waterman. Linear trees and RNA secondary structure. Discr. Appl. Math., 51:317–323, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  16. P. Stadler. private communication. unpublished.

    Google Scholar 

  17. R.P. Stanley. Differentiably finite power series. Eur. J. Combinator., 1:175–188, 1980.

    MATH  MathSciNet  Google Scholar 

  18. E.C. Titchmarsh. The theory of functions. Oxford University Press, NY, 1939.

    Google Scholar 

  19. B. Voß, R. Giegerich, and M. Rehmsmeier. Complete probabilistic analysis of RNA shapes. BMC Biology, 5(4):1–23, 2006.

    Google Scholar 

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Correspondence to Christian Reidys .

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Reidys, C. (2011). Combinatorial analysis. In: Combinatorial Computational Biology of RNA. Springer, New York, NY. https://doi.org/10.1007/978-0-387-76731-4_4

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