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Annali di Matematica Pura ed Applicata

, Volume 99, Issue 1, pp 155–182 | Cite as

Enumeration of rectangular arrays by length and coincidences

  • L. Carlitz
Article

Summary

Explicit formulas are obtained for the number of p-line arrays of integers (aij) (i=1, 2, ..., p; j=1, 2, ..., n) satisfying 1=ap1=...=a11⩽ap2⩽...a12⩽...⩽apn⩽...⩽a1n and a1j⩽j (j=1, 2, ..., n) and having k coincidences. (A coincidence is a column in which a1j=...=apj.)

Keywords

Explicit Formula Rectangular Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    R. Alter,Some remarks and results on Catalan numbers, Proceedings of the Second Louisiana Conference on Combinatories, Graph Theory and Computing, Baton Rouge, 1971, pp. 109–132.Google Scholar
  2. [2]
    L. Carlitz,Enumeration of two-line arrays, Fibonacci Quarterly,11 (1973), pp. 131–130.MathSciNetGoogle Scholar
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    N. E. Norlund,Vorlesungen über Differenzenrechnung, Springer, Berlin, 1925.Google Scholar
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    G. PólyaG. Szegö,Aufgaben und Lehrsötze aus der Analysis, vol. 1, Springer, Berlin, 1923.Google Scholar
  5. [5]
    J. Riordan,An Introduction to Combinatorial Analysis, Wiley, New York, 1958.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1974

Authors and Affiliations

  • L. Carlitz
    • 1
  1. 1.Durham

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