可推倒排列的刻劃與性質

Abstract

本論文在第一章首先會先簡單介紹 toppleable permutation，然後在第二章針對 Arvind Ayyer, Daniel Hathcock 與 Prasad Tetali 等人 [1] 所提出的 rtoppleable permutation 做更進一步的刻劃，另外提出一些與 Arvind Ayyer and Beáta Bényi [2] 所提出的論文之相同與相異之處，最後在第三章提出一個關於數列 t(n, r) 的新結果，還有關於 poly-Bernoulli number type B 和 type C 做 gamma positive 的一些研究與正在整理的猜想。In this paper, first we will introduce the toppleable permutation in Chapter 1, then we further describe the r-toppleable permutation proposed by Arvind Ayyer, Daniel Hathcock and Prasad Tetali et al.[1], also present some similarities and differenceswith the paper presented by Arvind Ayyer and Beáta Bényi [2] in Chapter 2, the third chapter presents a new result about the sequence t(n, r), as well as some researches and conjectures that are being sorted out about the poly-Bernoulli number type B and type C being gamma positive.