Enumerative combinatorics. Vol. 1. 2nd ed. (English) Zbl 1247.05003

Cambridge Studies in Advanced Mathematics 49. Cambridge: Cambridge University Press (ISBN 978-1-107-60262-5/pbk; 978-1-107-01542-5/hbk; 978-1-139-20056-1/ebook). xiii, 626 p. (2012).
The first edition of this book has become established as the standard introduction to enumerative combinatorics. Since the publication in 1986, the field has developed rapidly. The present new edition takes this fact into account.
The first chapter “What is enumerative combinatorics?” has been enlarged by six new sections which mainly treat permutation statistics but also \(q\)-analogues of permutations. The third chapter “Partially ordered sets” now includes additional sections on hyperplane arrangements, the \(cd\)-index, promotion and evacuations, and differential posets. The new edition comes with more than 350 new exercises; less difficult exercises are without solutions now.
See the reviews of the first editions in [Zbl 0945.05006; Zbl 0608.05001; Zbl 0889.05001].


05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration
06A07 Combinatorics of partially ordered sets
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