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arXiv · 1410.6601

Unimodality, log-concavity, real-rootedness and beyond

Petter Brändén
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Abstract

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. This is a draft of a chapter to appear in Handbook of Enumerative Combinatorics, published by CRC Press.

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Petter Brändén. 2014-10-24. Unimodality, log-concavity, real-rootedness and beyond. https://arxiv.org/abs/1410.6601

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