Lattice Path Combinatorics and Special Counting Sequences

From an Enumerative Perspective
1. Auflage 2024
ISBN: 978-1-032-67175-8
Verlag: CRC Press

Buch, Englisch, 119 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 436 g

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.

Zielgruppe

Postgraduate and Professional Reference

Autoren/Hrsg.

Song, Chunwei

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

1 Introduction  2 Combinatorial Statistics  3 Special Counting Sequences  4 Lattice Paths

Über Autor(innen)

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.