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Periodica Mathematica Hungarica

, Volume 20, Issue 2, pp 147–154 | Cite as

Arbres et suites majeures

  • P. Moszkowski
Article

Abstract

The major sequences of lengthn are defined as the words withn letters taken from the integers 1, 2, ⋯,n and containing at least

  1. 1.

    letter equal ton

     
  2. 2.

    letters equal or more thann − 1,⋯n − 1 letters equal or more than 2.

     

In Part 2 the major sequences of lengthn containing exactlyk letters equal ton are enumerated. Part 3 is devoted to the construction of a bijection between the trees withn + 1 vertices and the major sequences of lengthn. This bijection allows to give new proofs to the results in Part 2; moreover, a formula for the sequences written with exactlyk distinct letters is derived.

Mathematics subject classification numbers, 1980/1985

Primary 05A Secondary 05C 

Key words and phrases

Major sequence tree 

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Références

  1. [1]
    A. Cayley, A theorem on trees,Quart. J. Math. 23 (1889), 376–378.Google Scholar
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    L. E. Clarke, On Cayley's formula for counting trees,J. London Math. Soc. 33 (1958), 471–474.MR 20: 7282Google Scholar
  3. [3]
    G. Kreweras, Une famille de polynômes ayant plusieurs propriétés énumératives,Period. Math. Hungar. 11 (1980), 309–320.MR 82f: 05007Google Scholar
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    Y. Poupard,Codage et dénombrement de diverses structures apparentées à celle d'arbre, Cahiers du B.I.R.O., Institut de Statistique des Universités de Paris, 1971.Google Scholar
  5. [5]
    G. Quattrocchi, Su un problema di J. Dénes inerente certe successioni finite (On a problem of J. Dénes on certain finite sequences),Atti Sem. Mat. Fis. Univ. Modena 29 (1980), 1–9.MR 82m: 05003aGoogle Scholar

Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • P. Moszkowski
    • 1
  1. 1.Institut StatistiqueUniversité Paris VIParisFrance

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