Publication at Faculty of Mathematics and Physics |
2016
Abstract
A finite sequence of real numbers is called unimodal if it can be decomposed into a nondecreasing and a nonincreasing part. We focus on combinatorial sequences, in particular those consisting of binomial numbers or Stirling numbers of the first or second kind.
Apart from unimodality, we discuss the related notion of logarithmic convexity. We also demonstrate the relation between these topics and the classical Newton and Maclaurin inequalities, which are subsequently applied in the solution of a general version of the birthday paradox.