The author has wisely, in your reviewer’s opinion, chosen to view combinatorics as a tool to create data structures which lead naturally to algorithms, some of which may be near optimal, rather than creating a collection of supposedly optimal algorithms for specific problems. He uses combinatorial mathematics to develop a student’s intuitive understanding needed for the practical discussion of real algorithms to be used with a specific computer system.

The concept of linear order is used throughout the first 222 pages to bring unity to equivalence, hashing, Hasse and other diagrams, backtracking, set coverings, trees, partitions and related topics, various theories of sorting, combinatorial lists, ordered partitions, group theory, symmetry, recurrence relations, generating functions, networks and related combinatorial topics.

Pages 223 to 472 are then devoted to an intensive study of graphs and recursion, including the analysis of numerous puzzles, games, stacks, spanning trees, searching, matroids (and related polynomials), as well as matroid algorithms. The relationship between tree structure and recursion is well presented using numerous examples.

Any computer scientist or applied mathematician will be well advised to obtain a copy of this book, whether for teaching or learning. It is well suited for use by an instructor already familiar with combinatorics and graph theory since it presents many topics in unusual, informal ways that will appeal to the student. This does not imply that the author fails to provide proofs--he does very well in that department--but he frequently introduces topics and concepts so skillfully through examples that the reader is forced to produce the heart of the proof himself, informally, before the formal proof is encountered. It should be a fun text to use either as a student or as a professor, particularly if the class size is small enough so that an informal seminar approach can be used. Check a copy out of your library and examine it for yourself. I like it and you may also.