Wednesday, October 1, 2025
Time: 16:10-17:00
venue: Mathematics Building Room 527
Speaker: Prof. Hsing-Ming Chang (Department of Statistics, National Cheng Kung University)
Title: A probabilistic approach in understanding Eulerian number’s connection to Euler numbers
Abstract:
Everyone knows that Euler's number (e = 2.718…), having many expressions, is irrational and its decimal representation goes on infinitely without repeating. In contrast to the role of Euler’s number in mathematics, less is known about the Euler numbers and Eulerian number and the relationship of the two.
We present in this talk a method, using a Markov chain approach, to obtain the exact distribution of the number of peaks associated with a random permutation of {1, 2, . . . , n}. Not only the number of alternating permutations in the group of all permutations generated by {1, 2, . . . , n} for given n can be obtained, along the way, its connection to the number of descents (falls) is established through the distribution of peaks.
Reference