This is a text that defines "the number of ways there are of doing some well-defined operation." Covers permutations and combinations associated with elementary algebra, generating functions, the principle of inclusion and exclusion, the cycles of permutations, the theory of distributions, partitions, compositions, trees, and linear graphs; and permutations with restricted position. Includes problems. 1958 edition.
Here's a sample of other books in this Dover category
Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations by Wilhelm Magnus, Abraham Karrass, Donald Solitar A seminal, much-cited account of combinatorial group theory — co-authored by a distinguished teacher of mathematics and a pair of his colleagues — this text for graduate students features numerous helpful exercises. Second, revised 1976 edition.
Combinatory Analysis by Percy A. MacMahon Account of combinatory analysis theorems shows their connections and unites them as parts of a general doctrine. Topics include symmetric functions, theory of number compositions, more. 1915, 1916, and 1920 editions.
Combinatorial Enumeration by Ian P. Goulden, David M. Jackson Graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems, from elementary to research level, for discrete structures and their substructures. Full solutions to 350 exercises.
