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  1. Home > Articles & Issues >
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  3. Plane recursive tree ...
Conference paper

Plane recursive trees, Stirling permutations and an urn model

Svante Janson (1)
(1) Department of Mathematics [Uppsala]
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Imported on
May 10, 2017
Published on
December 31, 2007
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Proceedings
DOI
10.46298/dmtcs.3590
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https://about.hal.science/hal-authorisation-v1
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Plane recursive trees, Stirling permutations and an urn model

Svante Janson (1)
(1) Department of Mathematics [Uppsala]
Abstract
We exploit a bijection between plane recursive trees and Stirling permutations; this yields the equivalence of some results previously proven separately by different methods for the two types of objects as well as some new results. We also prove results on the joint distribution of the numbers of ascents, descents and plateaux in a random Stirling permutation. The proof uses an interesting generalized Pólya urn.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • Plane recursive trees
  • Stirling permutations
  • number of ascents
  • number of descents
  • urn model
  • generalized Pólya urn
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