本书主要概述了欧拉统计量的几个**进展,着重论述了欧拉统计量、峰统计量、交错子列统计量、上升平台统计量等相关的组合统计量,并利用形式文法理论探讨了一些经典的计数多项式。本书可供组合数学方向的研究生和相关学者阅读。
Chapter 1 Preliminary
1.1 Eulerian polynomials
1.2 Derivative polynomials
1.3 Peak polynomials
1.4 Alternating run polynomials
Chapter 2 Context-free grammars
2.1 Several classical examples
2.2 Ramanujan polynomials
2.3 Multivariate Eulerian polynomials
Chapter 3 Eulerian statistics on Stirling permutations
3.1 Introduction
3.2 The ascent-plateau statistics
3.3 A symmetric distribution
3.4 The flag ascent-plateau statistics
3.5 A partial gamma expansion
3.6 Dual Stirling permutations
Chapter 4 Eulerian statistics on simsun permutations
4.1 Introduction
4.2 Relationship to interior peaks
4.3 Interior peaks of simsun permutations
4.4 Signed simsun permutations
4.5 Even-signed simsun permutations
4.6 Simsun succesions and simsun patterns
4.7 Simsun permutations of the second kind
Bibliography