Periodic de Bruijn triangles: Exact and asymptotic results

Boris Shapiro, Michael Shapiro, Alek Vainshtein

Research output: Contribution to journalArticlepeer-review


We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.

Original languageEnglish
Pages (from-to)321-333
Number of pages13
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 6 Aug 2005

Bibliographical note

Funding Information:
The authors are grateful to Max–Planck-Institut für Mathematik, Bonn for its hospitality in Summer 2000 and to the Royal Institute of Technology, Stockholm for the financial support of the visit of A.V. to Stockholm in July–August 2001. Sincere thanks go to R. Ehrenborg, A. Laptev, H. Shapiro, A. Volberg and P. Yuditski for useful discussions.


  • Asymptotics
  • Generating function
  • Permutations
  • Up-down sequence

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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