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 mode 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 inteally, 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 mode 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 inteally, 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.

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