In this paper, we consider a new statistic on the set Sn of permutations of length n which records the number of vertical edges within their bargraph representations. In-deed, we determine the distribution of this statistic on a class of multi-permutations having Sn as a subset. We compute an explicit formula for the total number of vertical edges within all members of this class and also for the number of interior vertices in the corresponding bargraphs. A generating function formula is determined and some closely related statistics are considered. Finally, we show that the total number of vertical edges in all the members of Sn equals the number of runs in the members of Sn+1 by constructing an explicit bijection which applies more generally to multi-permutations.
Bibliographical noteFunding Information:
(B)This material is based upon work supported by the National Research Foundation under grant numbers 86329, 81021, respectively.
This material is based upon work supported by the National Research Foundation under grant numbers 86329, 81021, respectively.
© Institut für Informatik · Justus-Liebig-Universität Giessen.
- Generating functions
- Multi-set permutations
- Permutation statistics
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics