Combinatorics: Art and Philosophy

Combinatorics is about the art and philosophy with respect to “count without counting”. This is the dissertation of Dr. Chunwei Song at the University of Pennsylvania back in 2004. Herein various aspects of lattice path combinatorics are investigated, and the elegance of this beautiful subject is majestically demonstrated. For historical concerns, content in this volume is untouched from its original form as in the author''s submitted doctoral thesis.