Unimodality, log-concavity, real-rootedness and beyond. (English) Zbl 1327.05051

Bóna, Miklós (ed.), Handbook of enumerative combinatorics. Boca Raton, FL: CRC Press (ISBN 978-1-4822-2085-8/hbk; 978-1-4822-2086-5/ebook). Discrete Mathematics and its Applications, 437-483 (2015).
Summary: This is a survey on recent developments on unimodality, log-concavity and real-rootedness in combinatorics. Stanley and Brenti have written extensive surveys of various techniques that can be used to prove real-rootedness, log-concavity or unimodality. After a brief introduction, we will complement these surveys with a survey over some new techniques that have been developed, as well as problems and conjectures that have been solved.
For the entire collection see [Zbl 1314.05001].


05B35 Combinatorial aspects of matroids and geometric lattices
05A15 Exact enumeration problems, generating functions
11B75 Other combinatorial number theory
11B83 Special sequences and polynomials
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