1st Edition
Lattice Path Combinatorics and Special Counting Sequences From an Enumerative Perspective
This book endeavors to deepen our understanding of lattice path combinatorics, explore key types of special sequences, elucidate their interconnections, and concurrently champion the author's interpretation of the “combinatorial spirit”.
The author intends to give an up-to-date introduction to the theory of lattice path combinatorics, its relation to those special counting sequences that are important in modern combinatorial studies, such as the Catalan, Schröder, Motzkin, Delannoy numbers, and their generalized versions. Brief discussions of applications of lattice path combinatorics to symmetric functions and connections to the theory of tableaux are also included. Meanwhile, the author also presents an interpretation of the "combinatorial spirit" (i.e., "counting without counting", bijective proofs, and understanding combinatorics from combinatorial structures internally, etc.), hoping to shape the development of contemporary combinatorics.
The book will appeal to graduate students and advanced undergraduates studying combinatorics, discrete mathematics, or computer science.
1 Introduction 2 Combinatorial Statistics 3 Special Counting Sequences 4 Lattice Paths
Biography
Chunwei Song, a combinatorialist and graph theorist, is a professor of mathematics at Peking University. He received his Ph.D. from the University of Pennsylvania in 2004. After that, and before joining Peking University, he held faculty positions at Boston College, MA, and the Tokyo Institute of Technology in Japan. In 2010, he was a visiting associate professor at the University of Delaware. At Peking University, six students have received Ph.D. degrees under his supervision, specializing in the fields of lattice path combinatorics, extremal combinatorics, or mathematical philosophy.
