aequationes mathematicae

, Volume 23, Issue 1, pp 6–23 | Cite as

Sequence enumeration

  • I. P. Goulden
  • D. M. Jackson
Expository Paper

AMS (1980) subject classification

Primary 05A15 Secondary 15A15, 15A33 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    André, D.,Développements de séc. x et de tang. x. C.R. Acad. Sci. Paris88 (1879), 965–967.Google Scholar
  2. [2]
    André, D.,Mémoire sur les permutations alternées. J. Math. Pures Appl.7 (1881), 167–184.Google Scholar
  3. [3]
    Carlitz, L.,Enumeration of sequences by rises and falls. Duke Math. J.39 (1972), 267–280.CrossRefGoogle Scholar
  4. [4]
    Carlitz, L. andScoville, R.,Generating functions for certain types of permutations. J. Combin. Theory Ser. A18 (1975), 262–275.CrossRefGoogle Scholar
  5. [5]
    Cartier, P. andFoata, D.,Problèmes combinatoires de commutation et réarrangements. Lecture Notes in Mathematics Vol. 85. Springer, Berlin, 1969.Google Scholar
  6. [6]
    Foata, D. andSchützenberger, M. P.,Théorie géométrique des polynômes Eulériens. Lecture Notes in Mathematics Vol. 138. Springer, Berlin, 1970.Google Scholar
  7. [7]
    Gessel, I. M.,Generating functions and enumeration of sequences. Doctoral thesis, 1977, Massachusetts Institute of Technology, Cambridge, Massachusetts.Google Scholar
  8. [8]
    Goulden, I. P.,Combinatorial decomposition in the theory of algebraic enumeration. Doctoral thesis, 1979, University of Waterloo, Waterloo, Ontario, Canada.Google Scholar
  9. [9]
    Goulden, I. P. andJackson, D. M.,A logarithmic connection for circular permutation enumeration. Submitted for publication.Google Scholar
  10. [10]
    Jackson, D. M. andAleliunas, R.,Decomposition based generating functions for sequences. Canad. J. Math.29 (1977), 971–1009.Google Scholar
  11. [11]
    Jackson, D. M. andGoulden, I. P.,A formal calculus for the enumerative system of sequences I. Combinatorial theorems. Stud. Appl. Math.61 (1979), 141–178.Google Scholar
  12. [12]
    Jackson, D. M. andGoulden, I. P.,A formal calculus for the enumerative system of sequences II. Applications. Stud. Appl. Math.61 (1979), 245–277.Google Scholar
  13. [13]
    Jackson, D. M. andGoulden, I. P.,A formal calculus for the enumerative system of sequences III. Further developments. Stud. Appl. Math.62 (1980), 113–142.Google Scholar
  14. [14]
    Jackson, D. M. andGoulden, I. P.,Algebraic methods for permutations with prescribed patterns. Advances in Math.42 (1981), 113–135.CrossRefGoogle Scholar
  15. [15]
    Jackson, D. M., Jeffcott, B. andSpears, W. T.,The enumeration of sequences with respect to structures on a bipartition. Discrete Math.30 (1980), 133–149.CrossRefGoogle Scholar
  16. [16]
    Lucas, É.,Théorie des nombres. Paris, 1891. Reprinted by Blanchard, 1961.Google Scholar
  17. [17]
    MacMahon, P. A.,Combinatory Analysis, Vol. I. Chelsea, New York, 1960.Google Scholar
  18. [18]
    Montmort, P. R.,Essai d'analyse sur les jeux de hazard. Paris, 1708.Google Scholar
  19. [19]
    Netto, E.,Lehrbuch der Combinatorik. Chelsea, New York, 1958.Google Scholar
  20. [20]
    Reilly, J. W.,An enumerative combinatorial theory of formal power series. Doctoral thesis, 1977, University of Waterloo, Waterloo, Ontario, Canada.Google Scholar
  21. [21]
    Riordan, J.,An introduction to combinatory analysis. Wiley, New York, 1958.Google Scholar
  22. [22]
    Roselle, D. P.,Permutations by number of rises and successions. Proc. Amer. Math. Soc.19 (1968), 8–16.Google Scholar
  23. [23]
    Smirnov, N. V., Sarmarov, O. V., andZaharov, V. K.,A local limit theorem for transition numbers in a markov chain and its applications. Soviet Math. Dokl. 7, 563–566; Dokl. Akad. Nauk SSSR167 (1966), 1238–1241.Google Scholar
  24. [24]
    Stanley, R. P.,Binomial posets, Möbius inversion and permutation enumeration. J. Combin. Theory Ser. A20 (1976), 336–356.CrossRefGoogle Scholar
  25. [25]
    Tanny, S. M.,Permutations and successions. J. Combin. Theory Ser. A21 (1976), 196–202.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • I. P. Goulden
    • 1
    • 2
  • D. M. Jackson
    • 1
    • 2
  1. 1.Department of StatisticsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

Personalised recommendations