The moduli space of n tropically collinear points in Rd.

Develin, Mike. "The moduli space of n tropically collinear points in Rd.." Collectanea Mathematica 56.1 (2005): 1-19. <http://eudml.org/doc/41817>.

@article{Develin2005,
abstract = {The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension d = 3 and compute is homology in this case, conjecturing that this complex is shellable in general. We also investigate the space of d x n matrices of Barvinok rank two, a subcomplex directly related to optimization, giving a complete description of this subcomplex in the case d = 3.},
author = {Develin, Mike},
journal = {Collectanea Mathematica},
keywords = {Geometría discreta; Politopos; Espacio de moduli; Matrices; tropical semi-ring; Barvinok rank; tropical Grassmannian; phylogenetic tree},
language = {eng},
number = {1},
pages = {1-19},
title = {The moduli space of n tropically collinear points in Rd.},
url = {http://eudml.org/doc/41817},
volume = {56},
year = {2005},
}

TY - JOUR
AU - Develin, Mike
TI - The moduli space of n tropically collinear points in Rd.
JO - Collectanea Mathematica
PY - 2005
VL - 56
IS - 1
SP - 1
EP - 19
AB - The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension d = 3 and compute is homology in this case, conjecturing that this complex is shellable in general. We also investigate the space of d x n matrices of Barvinok rank two, a subcomplex directly related to optimization, giving a complete description of this subcomplex in the case d = 3.
LA - eng
KW - Geometría discreta; Politopos; Espacio de moduli; Matrices; tropical semi-ring; Barvinok rank; tropical Grassmannian; phylogenetic tree
UR - http://eudml.org/doc/41817
ER -