# The moduli space of n tropically collinear points in Rd.

Collectanea Mathematica (2005)

- Volume: 56, Issue: 1, page 1-19
- ISSN: 0010-0757

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topDevelin, 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 -

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