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Generatingfunctionology. 2nd ed. (English) Zbl 0831.05001

Boston, MA: Academic Press. x, 228 p. (1994).
From the preface: “This edition contains several new areas of application in Chapter 4, many new problems and solutions, a number of improvements in the presentation, and corrections.”
For a review of the first edition see Zbl 0689.05001.

MSC:

05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05A15 Exact enumeration problems, generating functions

Citations:

Zbl 0689.05001
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Online Encyclopedia of Integer Sequences:

Bell or exponential numbers: number of ways to partition a set of n labeled elements.
Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.
Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].
Number of connected labeled graphs with n nodes.
Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2.
Number of square permutations of n elements.
Pascal’s triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n.
Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
Irregular triangle of numbers read by rows: {binomial(n-k, k), n >= 0, 0 <= k <= floor(n/2)}; or, triangle of coefficients of (one version of) Fibonacci polynomials.
Nearest integer to n!/(2*log(2)^(n+1)).
Number of derangements of n where minimal cycle size is at least 3.
Number of labeled graphs with 2-colored nodes where black nodes are only connected to white nodes and vice versa.
Number of labeled bipartite graphs with n nodes.
Number of derangements of n where minimal cycle size is at least 4.
Number of permutations of n elements admitting a cube root.
Number of permutations of n elements admitting a fourth root.
Triangle read by rows: T(n,k) (0<=k<=n) is the number of labeled graphs having k blue nodes and n-k green ones and only nodes of different colors can be joined by an edge.
Number of labeled graphs having n blue nodes and n green ones, where edges join only nodes of different colors.
Number of permutations on n points admitting a fifth root.
Number of permutations on n points admitting a sixth root.
Number of permutations on n points admitting a seventh root.
Number A(n,k) of permutations on [n] that are the k-th power of a permutation; square array A(n,k), n>=0, k>=0, read by antidiagonals.
Number of permutations on [n] admitting an eighth root.
Number of permutations on [n] admitting a ninth root.
Number of permutations on [n] admitting a tenth root.
Number of permutations on [n] that are the n-th power of a permutation.
Number of permutations of {1,2,...,n} having equal numbers of 1-cycles and 2-cycles.