Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective

Lattice Path Combinatorics and Special Counting Sequences: From an Enumerative Perspective
by: Chunwei Song (Author)
Publisher: CRC Press
Edition: 1st
Publication Date: 2024/9/17
Language: English
Print Length: 105 pages
ISBN-10: 1032671750
ISBN-13: 9781032671758
Book Description
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.
About the Author
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. Read more