aequationes mathematicae

, Volume 10, Issue 1, pp 10–22 | Cite as

Mappings of acyclic and parking functions

  • Dominique Foata
  • John Riordan
Research Papers
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Revised:

Abstract

The two functions in question are mappings: [n]→[n], with [n] = {1, 2,⋯,n}. The acyclic function may be represented by forests of labeled rooted trees, or by free trees withn + 1 points; the parking functions are associated with the simplest ballot problem. The total number of each is (n + 1)n-1. The first of two mappings given is based on a simple mapping, due to H. O. Pollak, of parking functions on tree codes. In the second, each kind of function is mapped on permutations, arising naturally from characterizations of the functions. Several enumerations are given to indicate uses of the mappings.

Keywords

Rooted Tree Simple Mapping Tree Code Free Tree Parking Function 
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.
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Copyright information

© Birkhüuser Verlag 1974

Authors and Affiliations

  • Dominique Foata
    • 1
    • 2
  • John Riordan
    • 1
    • 2
  1. 1.University of FloridaGainesvilleUSA
  2. 2.Rockefeller UniversityNew YorkUSA

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