On the polyhedral cones of convex and concave vectors

2013/12/02 by Foldes, Stephan, Major, Laszlo
#05A20 #05D05 #15A39 #15B48 #52A40 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1312.0561

Abstract

Convex or concave sequences of n positive terms, viewed as vectors in n-space, constitute convex cones with 2n-2 and n extreme rays, respectively. Explicit description is given of vectors spanning these extreme rays, as well as of non-singular linear transformations between the positive orthant and the simplicial cones formed by the positive concave vectors. The simplicial cones of monotone convex and concave vectors can be described similarly.

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