Lattice Path Combinatorics and Special Counting Sequences

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, Schrder, 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.