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Algebraic enumeration. (English) Zbl 0853.05002
Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2. Amsterdam: Elsevier (North-Holland). 1021-1061 (1995).
That part of combinatorics dealing with enumeration is a fascinating subject full of weird coincidences and amazing parallels. This chapter is an impressive survey of algebraic enumeration by two of the leading experts. The important methods and tools are described in detail along with numerous illustrations. For example, the reader will find ample treatments of generating functions, bijections, Lagrange inversion, the transfer matrix method, inclusion-exclusion, Möbius inversion and Pólya’s theorem. Numerous applications are provided to count fundamental combinatorial structures such as various types of permutations, partitions, walks in space, and graphs. There is a helpful list of references for the reader who seeks to delve further into the mysteries of this vast and extraordinary area.
For the entire collection see [Zbl 0833.05001].

05A15 Exact enumeration problems, generating functions
05E05 Symmetric functions and generalizations
05A17 Combinatorial aspects of partitions of integers