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Combinatorial Mathematics X pp 230–243Cite as

Stochastic processes and combinatoric identities

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1036))

Abstract

Despite the existence of such salient successes as the use of ergodic theory to establish Szemerédi's theorem, dynamical systems and stochastic processes have not been widely employed in the derivation of combinatoric results. This paper offers instances of what the authors believe should be a more widespread tool in the routine analysis of combinatoric problems.

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References

  1. E.S. Andersen, On sums of symmetrically dependent random variables. Skand. Aktuaretid. 36 (1953), 123–138.

    MathSciNet  MATH  Google Scholar 

  2. E.S. Andersen, On the fluctuation of sums of independent random variables. Math. Skand. 1 (1953), 263–285.

    MATH  Google Scholar 

  3. E.S. Andersen, On the fluctuation of sums of independent random variables II. Math. Skand. 2 (1954), 195–223.

    MATH  Google Scholar 

  4. A.F. Antippa and N.K. Toan, Topological solution for systems of simultaneous linear equations. J. Math. Phys. 20 (1979), 2375–2379.

    Article  MathSciNet  MATH  Google Scholar 

  5. A.F. Antippa and N.K. Toan, Topological solution of ordinary and partial finite difference equations. J. Math. Phys. 21 (1980), 2475–2480.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. Erdös and J. Spencer, Probabilistic Methods in Combinatorics. Academic Press, New York (1974).

    MATH  Google Scholar 

  7. W. Feller, An introduction to probability theory and its applications, Vol. I, 3rd edition. Wiley and Sons, New York (1968).

    MATH  Google Scholar 

  8. H. Furstenberg, Recurrence relations in ergodic theory and combinatorial number theory. Princeton U.P., Princeton (1981).

    Book  MATH  Google Scholar 

  9. E. Hauer and J.G.C. Templeton, Queueing in Lanes. Trans. Sci., 6 (1972), 247–259.

    Article  Google Scholar 

  10. W. Henderson, R.W. Kennington and C.E.M. Pearce, A second look at a problem of queueing in lanes. To appear in Transportation Science.

    Google Scholar 

  11. C. Jordan, Calculus of finite differences, 2nd edition. Chelsea Publ. Co., New York (1947).

    MATH  Google Scholar 

  12. S. Karlin, A first course in stochastic processes. Academic Press, New York (1966).

    Google Scholar 

  13. V.F. Kolchin and V.P. Chistyakov, Combinatorial problems in probability theory. Results of Science and Technology, Ser: Prob. Theory, Math. Stats, Theor. Cybernetics (All Union Inst. of Scientific and Tech. Info., Moscow), 11 (1974), 5–54 (in Russian).

    Google Scholar 

  14. V.F. Kolchin, B.A. Sevast'yanov and V.P. Chistyakov, Random Allocations. V.H. Winston (Wiley), Washington (1978).

    MATH  Google Scholar 

  15. D.J. Newman and L. Shepp, The double dixie cup problem. Amer. Math. Monthly, 67 (1960), 58–61).

    Article  MathSciNet  MATH  Google Scholar 

  16. C.E.M. Pearce and M.S. Keane, On normal numbers. J. Aust. Math. Soc. (A), 32 (1982), 79–87.

    Article  MathSciNet  MATH  Google Scholar 

  17. F. Pollaczek, Fonctions caractéristiques de certaines répartitions definies au moyen de la notion d'ordre. Application à la théorie des attentes. Compt. Rend. Acad. Sci. Paris, 234 (1952), 2234–2236.

    MATH  Google Scholar 

  18. G. Polya, Eine Wahrscheinlichkeitsaufgabe zur Kundenwerbung. Zeit. für angewandte Math. und Mech., 10 (1930), 96–97.

    Article  MATH  Google Scholar 

  19. S.C. Port, An elementary probability approach to fluctuation theory. J. Math. Anal. and Applic., 6 (1963), 109–151.

    Article  MathSciNet  MATH  Google Scholar 

  20. G.-C. Rota, On the foundations of combinatorial theory I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie, 2 (1964), 340–368.

    Article  MathSciNet  MATH  Google Scholar 

  21. J.Th. Runnenburg, On the use of the method of collective marks in queueing theory. Proceedings of the symposium on congestion theory, Ed. W.L. Smith and W.E. Wilkinson, Univ. of N. Carolina, Chapel Hill (1965), 399–438.

    Google Scholar 

  22. W. Schmidt, On normal numbers. Pacific J. Math., 10 (1960), 661–672.

    Article  MathSciNet  MATH  Google Scholar 

  23. F. Spitzer, A combinatorial lemma and its application to probability theory. Transac. Amer. Math. Soc., 82 (1956), 323–339.

    Article  MathSciNet  MATH  Google Scholar 

  24. L. Takács, Combinatorial methods in the theory of stochastic processes. Wiley and Sons, New York (1967).

    MATH  Google Scholar 

  25. R.J. Wilson, Combinatorial Mathematics and its Applications. Ed. D.J.A. Walsh, Academic Press, New York (1971), 315–333.

    Google Scholar 

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Authors
  1. W. Henderson
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  2. R. W. Kennington
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  3. C. E. M. Pearce
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Editor information

Louis Reynolds Antoine Casse

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© 1983 Springer-Verlag

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Henderson, W., Kennington, R.W., Pearce, C.E.M. (1983). Stochastic processes and combinatoric identities. In: Casse, L.R.A. (eds) Combinatorial Mathematics X. Lecture Notes in Mathematics, vol 1036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071522

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  • DOI: https://doi.org/10.1007/BFb0071522

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12708-6

  • Online ISBN: 978-3-540-38694-0

  • eBook Packages: Springer Book Archive

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