We extend results of Wagner [8] and Fomin, Kratsch, and Novelle [6] on monotone partitions of permutations. We show that partitioning a sequence of distinct integers into unimodal subsequences is NP-complete and that a minimum unimodal partition is 3.42-approximable in polynomial time.

A distortion theory is developed for S−unimodal maps. It will be used to get some geometric understanding of invariant Cantor sets. In particular attracting Cantor sets turn out to have Lebesgue measure zero. Furthermore the ergodic behavior of S−unimodal maps is classified according to a distortion property, called the Markov-property.

In this paper we characterize the existence of periodic points of odd period greater than one for unimodal mappings of an interval onto itself. The interesting juxtaposition of this condition with the occurrence in inverse limits of the well-known Brouwer-Janiszewski-Knaster continuum is explored. Also obtained is a characterization of indecomposability of certain inverse limits using a single ...

We consider L1-isotonic regression and L∞ isotonic and unimodal regression. For L1isotonic regression, we present a linear time algorithm when the number of outputs are bounded. We extend the algorithm to construct an approximate isotonic regression in linear time when the output range is bounded. We present linear time algorithms for L∞ isotonic and unimodal regression.