Riordan, John An introduction to combinatorial analysis. (English) Zbl 0078.00805 Wiley Publicatlon in Mathematical Statistics. New York: John Wiley & Sons, Inc.; London: Chapman & Hall, Ltd. x, 244 p. (1958). Reviewer: A. Sade Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 12 ReviewsCited in 709 Documents MSC: 05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics 05Axx Enumerative combinatorics 05A05 Permutations, words, matrices 05A15 Exact enumeration problems, generating functions 05A17 Combinatorial aspects of partitions of integers 05C05 Trees 05C99 Graph theory Keywords:combinatorics; permutations; combinations; generating functions; linear recurrences; moment generating functions; Stirling numbers; derivatives of composite functions; Bell polynomials; method of inclusion and exclusion; enumeration of permutations; distribution; occupancy problems; elementary theory of partitions; ordered partitions; enumeration theory of Pólya; graph enumeration; permutations with restricted positions × Cite Format Result Cite Review PDF Digital Library of Mathematical Functions: §1.4(iii) Derivatives ‣ §1.4 Calculus of One Variable ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods §26.14(ii) Generating Functions ‣ §26.14 Permutations: Order Notation ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.18 Counting Techniques ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.3(iii) Recurrence Relations ‣ §26.3 Lattice Paths: Binomial Coefficients ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.3(ii) Generating Functions ‣ §26.3 Lattice Paths: Binomial Coefficients ‣ Properties ‣ Chapter 26 Combinatorial Analysis Chapter 26 Combinatorial Analysis Online Encyclopedia of Integer Sequences: Number of degree-n even permutations of order dividing 2. Triangle read by rows of Stirling numbers of first kind, s(n,k), n >= 1, 1 <= k <= n. Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n. Triangle read by rows: a(n,k) = binomial(k,n-k). Triangle read by rows: T(n,k) is the number of partially labeled trees with n nodes, k of which are labeled, 0 <= k <= n. Triangle of number of node labeled trees by number of nodes and number of labels. Triangle of Stirling numbers of 2nd kind, S(n,k), n >= 0, 0 <= k <= n. Triangle of Stirling numbers of first kind, s(n,k), n >= 0, 0 <= k <= n. Number of degree-n even permutations of order dividing 8. Number of degree-n even permutations of order dividing 10. Triangle read by rows: counts permutations by number of big descents. Number of degree-n even permutations of order dividing 12