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.
Bibliographical noteFunding 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.
- Generating function
- Up-down sequence
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics