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On the ordering, ranking, and random generation of basic combinatorial sets

Partitions Et Algorithmes Combinatoires

Part of the Lecture Notes in Mathematics book series (LNM,volume 579)

Abstract

A model for linearly ordering basic classes of combinatorial sets is developed in terms of chains of partitions. In this context general procedures for locating the position of an object given the object (ranking) and for constructing an object given its position (unranking) are described. A general method of associating a labeled tree with a chain of partitions together with a reduction operation producing classes of labeled graphs from trees is presented. These latter operations relate these ideas to a general setting for sequencing, ranking, and selection algorithms due to H. S. Wilf.

Keywords

  • Linear Order
  • Label Graph
  • Label Tree
  • Combinatorial Object
  • Natural Identification

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.

Research supported by N. S. F. Grant MCS 74-02714-A02

Author at present on leave to University of Minnesota, Minneapolis, Minnesota, 55455, from University of California, San Diego, La Jolla, California, 92093.

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References

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© 1977 Springer-Verlag

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Williamson, S.G. (1977). On the ordering, ranking, and random generation of basic combinatorial sets. In: Foata, D. (eds) Combinatoire et Représentation du Groupe Symétrique. Lecture Notes in Mathematics, vol 579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090026

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  • DOI: https://doi.org/10.1007/BFb0090026

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08143-2

  • Online ISBN: 978-3-540-37385-8

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