On Distribution of the Number of Peaks and the Euler Numbers of Permutations

James C. Fu, Wan Chen Lee, Hsing Ming Chang

研究成果: Article同行評審

1 引文 斯高帕斯(Scopus)

摘要

Using the language of runs and patterns, a peak in a sequence of integers can be interpreted as observing a fall (or descent) immediately after a rise (or ascent). In this paper, we obtain the exact distribution of the number of peaks in a permutation by using the nonhomogeneous finite Markov chain imbedding technique and an insertion procedure. As a byproduct, we also obtain the Euler numbers, which are a sequence of the number of alternating permutations. The method is extended to obtaining the joint distribution of the number of peaks and the number of falls. Several numerical examples are given to illustrate our theoretical results.

原文English
文章編號46
期刊Methodology and Computing in Applied Probability
25
發行號2
DOIs
出版狀態Published - 2023 6月

All Science Journal Classification (ASJC) codes

  • 統計與概率
  • 一般數學

指紋

深入研究「On Distribution of the Number of Peaks and the Euler Numbers of Permutations」主題。共同形成了獨特的指紋。

引用此