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Restrictive Patterns of Combinatorial Structures via Comparative Analysis

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Abstract

Asymptotic probabilities of decomposable combinatorial structures with a fortiori prescribed properties are studied as the sizes unboundedly increase. A comparative analysis of the power series coefficients is applied.

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References

  1. Arratia, R., Barbour, A.D., Tavarée, S.: Logarithmic Combinatorial Structures: A Probabilistic Approach. European Mathematical Society, Züurich (2003)

  2. Barbour, A.D., Póosfai, A.: Couplings for irregular combinatorial assemblies. In: Barbour, A., Chan, H.P., Siegmund, D. (eds.) Probability Approximations and Beyond. Lecture Notes in Statist., Vol. 205, pp. 3–12. Springer, New York (2012)

  3. Barbour, A.D., Nietlispach, B.: Approximation by the Dickman distribution and quasilogarithmic combinatorial structures. Electronic J. Probab. 16, #P29 (2011)

  4. Bender E.A.: Asymptotic methods in enumeration. SIAM Rev. 16(4), 485–515 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  5. Betz, V., Ueltschi, D.: Spatial random permutations with small cycle weights. Probab. Theory Related Fields 149(1-2), 191–222 (2011)

  6. Braaksma B.L.J., Stark D.: A Darboux-type theorem for slowly varying functions. J. Combin. Theory Ser. A 77(1), 51–66 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dong L., Gao Z., Panario D.: Enumeration of decomposable combinatorial structures with restricted patterns. Ann. Combin. 12(4), 357–372 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ercolani N.M., Ueltschi D.: Cycle structure of random permutations with cycle weights. Random Structures Algorithms 44(1), 109–133 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ewens W.J.: The sampling theory of selectively neutral alleles. Theoret. Population Biology 3, 87–112 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  10. Flajolet P., Odlyzko A.: Singularity analysis of generating functions. SIAM J. Discrete Math. 3(2), 216–240 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Flajolet P., Sedgewick R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  12. Manstavičius E.: Mappings on decomposable combinatorial structures: analytic approach. Combin. Probab. Comput. 11(1), 61–78 (2002)

    MATH  MathSciNet  Google Scholar 

  13. Manstavičius E.: An analytic method in probabilistic combinatorics. Osaka J. Math. 46(1), 273–290 (2009)

    MATH  MathSciNet  Google Scholar 

  14. Manstavičius E.: Total variation approximation for random assemblies and functional limit theorem. Monatsh. Math. 161(3), 313–334 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  15. Manstavičius, E.: On total variation approximations for random assemblies. In: Broutin, N., Devroye, L. (eds.) 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA’12), pp. 97–108. Assoc. Discrete Math. Theor. Comput. Sci., Nancy (2012)

  16. Yakymiv A.L.: Permutations with cycle lengths in a given set. Diskret. Mat. 1(1), 125–134 (1989)

    MathSciNet  Google Scholar 

  17. Zacharovas V.: Voronoi summation formulae and multiplicative functions. Ramanujan J. 24(3), 289–329 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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  1. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania

    Eugenijus Manstavičius

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  1. Eugenijus Manstavičius
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Manstavičius, E. Restrictive Patterns of Combinatorial Structures via Comparative Analysis. Ann. Comb. 19, 545–555 (2015). https://doi.org/10.1007/s00026-015-0275-8

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  • DOI: https://doi.org/10.1007/s00026-015-0275-8

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