Cones of elementary imsets and supermodular functions: a review and some new results
Statistics Theory
2013-01-11 v1 Statistics Theory
Abstract
In this paper we give a review of the method of imsets introduced by Studeny (2005) from a geometric point of view. Elementary imsets span a polyhedral cone and its dual cone is the cone of supermodular functions. We review basic facts on the structure of these cones. Then we derive some new results on the following topics: i) extreme rays of the cone of standardized supermodular functions, ii) faces of the cones, iii) small relations among elementary imsets, and iv) some computational results on Markov basis for the toric ideal defined by elementary imsets.
Keywords
Cite
@article{arxiv.1109.2408,
title = {Cones of elementary imsets and supermodular functions: a review and some new results},
author = {Takuya Kashimura and Tomonari Sei and Akimichi Takemura and Kentaro Tanaka},
journal= {arXiv preprint arXiv:1109.2408},
year = {2013}
}