@article{10902/34559,
year = {2018},
url = {https://hdl.handle.net/10902/34559},
abstract = {We investigate a version of Viro's method for constructing polynomial systems with many positive solutions, based on regular triangulations of the Newton polytope of the system. The number of positive solutions obtained with our method is governed by the size of the largest positively decorable subcomplex of the triangulation. Here, positive decorability is a property that we introduce and which is dual to being a subcomplex of some regular triangulation. Using this duality, we produce large positively decorable subcomplexes of the boundary complexes of cyclic polytopes. As a byproduct, we get new lower bounds, some of them being the best currently known, for the maximal number of positive solutions of polynomial systems with prescribed numbers of monomials and variables. We also study the asymptotics of these numbers and observe a log-concavity property.},
organization = {The second author's research was partially supported by grant MTM2014-54207-P of the Spanish Ministry of Science, by the Einstein Foundation Berlin, and, while he was in residence at the Mathematical Sciences
Research Institute in Berkeley, California during the Fall 2017 semester, by the Clay Institute and the National
Science Foundation (grant DMS-1440140).},
publisher = {Society for Industrial and Applied Mathematics},
publisher = {SIAM Journal on Applied Algebra and Geometry, 2018, 2(4), 620-645},
title = {A polyhedral method for sparse systems with many positive solutions},
author = {Bihan, Frêdêric and Santos, Francisco and Spaenlehauer, Pierre Jean},
}