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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 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, and more), hoping to shape the development of contemporary combinatorics.
Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective will appeal to graduate students and advanced undergraduates studying combinatorics, discrete mathematics, or computer science.
List of contents
1 Introduction 2 Combinatorial Statistics 3 Special Counting Sequences 4 Lattice Paths
About the author
Chunwei Song, a combinatorialist and graph theorist, is a professor of mathematics at Peking University. He received his PhD from the University of Pennsylvania in 2004. He also held faculty positions at Boston College, MA and the Tokyo Institute of Technology, Japan. In 2010, he was a visiting associate professor at the University of Delaware. At Peking University, six students have received PhD degrees under his supervision, specializing in the fields of lattice path combinatorics, extremal combinatorics, or mathematical philosophy.
Summary
This book endeavors to deepen our understanding of lattice path combinatorics, to explore key types of special sequences, to elucidate their interrelations, and at the same time to advocate the author's interpretation of the "combinatorial spirit".
