Enumeration of Partitions by Long Rises , Levels , and Descents

  title={Enumeration of Partitions by Long Rises , Levels , and Descents},
  author={Toufik Mansour},
When the partitions of [n] = {1, 2, . . . , n} are identified with the restricted growth functions on [n], under a known bijection, certain enumeration problems for classical word statistics are formulated for set partitions. In this paper we undertake the enumeration of partitions of [n] with respect to the number of occurrences of rises, levels and descents, of arbitrary integral length not exceeding n. This approach extends previously known cases. We obtain ordinary generating functions for… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 17 references

Enumeration of partitions by rises

  • T. Mansour, A. O. Munagi
  • levels and descents, Proceedings of the Fifth…
  • 2007
Highly Influential
3 Excerpts

The Theory of Partitions

  • G. E. Andrews
  • Cambridge University Press
  • 1998

Enumeration of compositions by rises

  • L. Carlitz
  • falls and levels, Math. Nachr. 77
  • 1977
1 Excerpt

Enumeration of permutations by rises

  • L. Carlitz, R. Scoville
  • falls, rising maxima and falling maxima, Acta…
  • 1974
1 Excerpt

Similar Papers

Loading similar papers…