A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Tropical linear spaces and tropical convexity
[article]

2015
*
arXiv
*
pre-print

It is not difficult to see that each such

arXiv:1505.02045v1
fatcat:astlrjo4urer7fjokzoz776rca
*space*is*tropically**convex*, i.e. closed under*tropical**linear*combinations. ... In classical geometry, a*linear**space*is a*space*that is closed under*linear*combinations. ... One might then be tempted to define a*tropical**linear**space*as a*space*that is closed under*tropical**linear*combinations. This property is well-known under the name of*tropical**convexity*. ...##
###
Tropical Linear Spaces and Tropical Convexity

2015
*
Electronic Journal of Combinatorics
*

It is not difficult to see that each such

doi:10.37236/5271
fatcat:3aoatw4drfgflcgeol2mxxl4ha
*space*is*tropically**convex*, i.e. closed under*tropical**linear*combinations. ... In classical geometry, a*linear**space*is a*space*that is closed under*linear*combinations. ... In other words, X is the quotient of a*space*closed under*tropical**linear*combinations if*and*only if X is supported on a*tropical**linear**space*. ...##
###
Convexity in Tree Spaces

2017
*
SIAM Journal on Discrete Mathematics
*

We study the geometry of metrics

doi:10.1137/16m1079841
fatcat:timxs3tcg5c6pkmliy2sz2dpza
*and**convexity*structures on the*space*of phylogenetic trees, which is here realized as the*tropical**linear**space*of all ultrametrics. ...*Tropical**convexity**and*the*tropical*metric behave better. They exhibit properties desirable for geometric statistics, such as geodesics of small depth. ... We thank Simon Hampe, Andrew Francis*and*Megan Owen for helpful conversations. ...##
###
Affine Buildings and Tropical Convexity
[article]

2007
*
arXiv
*
pre-print

The notion of

arXiv:0706.1918v1
fatcat:buwv765yk5erdmc6gkhjmdsd4u
*convexity*in*tropical*geometry is closely related to notions of*convexity*in the theory of affine buildings. ... While the original inspiration was the work of Dress*and*Terhalle in phylogenetics,*and*of Faltings, Kapranov, Keel*and*Tevelev in algebraic geometry, our*tropical*algorithms will also be applicable to ... The*tropical**linear**space*L p is*tropically**convex*,*and*it can be represented as a*tropical*lattice polytope as follows. ...##
###
Tropicalizing the positive semidefinite cone

2014
*
Proceedings of the American Mathematical Society
*

We also show that the

doi:10.1090/s0002-9939-2014-12428-2
fatcat:pc4uk7pns5c57kmduby47ocjam
*tropical*PSD cone is the*tropical**convex*hull of the set of symmetric matrices of*tropical*rank one*and*that every*tropical*PSD matrix can be factored as a*tropical*product of a matrix ...*and*its transpose. ... All matrices in the*linear**space*is obtained from the all-zero matrix, which has*tropical*rank one, by*tropically*scaling rows*and*columns simultaneously,*and**tropical*scaling does not change the*tropical*...##
###
Tropical Principal Component Analysis and its Application to Phylogenetics
[article]

2017
*
arXiv
*
pre-print

In one approach, we study the Stiefel

arXiv:1710.02682v2
fatcat:ib222ntxuzaendledj43ajb3la
*tropical**linear**space*of fixed dimension closest to the data points in the*tropical*projective torus; in the other approach, we consider the*tropical*polytope with ... Here we define*and*analyze two analogues of principal component analysis in the setting of*tropical*geometry. ... The authors thank Bernd Sturmfels (UC Berkeley*and*MPI Leipzig) for many helpful conversations. ...##
###
Algorithms and Effectivity in Tropical Mathematics and Beyond (Dagstuhl Seminar 16482)

2017
*
Dagstuhl Reports
*

This report documents the Dagstuhl Seminar on Algorithms

doi:10.4230/dagrep.6.11.168
dblp:journals/dagstuhl-reports/GaubertGJT16
fatcat:xrlmqx4cpjckhfayqbdyyy63py
*and*Effectivity in*Tropical*Mathematics*and*Beyond, which took place from November 27 -December 02, 2016. ... Examples include:*Tropical*arithmetic (Min or Max -it's your choice!),*tropical**convex*hull computations,*tropical**linear**spaces*,*tropical*polynomials*and**tropical*hypersurfaces. ... As an application we obtain a dimension bound for the moduli*space*of those*tropical**linear**spaces*, the Dressian. ...##
###
Local Tropical Linear Spaces

2013
*
Discrete & Computational Geometry
*

We also study a certain class of

doi:10.1007/s00454-013-9519-8
fatcat:n7m3jyznjjap7kkrm7z7fc64je
*tropical**linear**spaces*that we call conical*tropical**linear**spaces*,*and*we give a simple proof that they satisfy Speyer's f-vector conjecture. ... In this paper we study general*tropical**linear**spaces*locally: For any basis B of the matroid underlying a*tropical**linear**space*L, we define the local*tropical**linear**space*L_B to be the subcomplex of ... Local*Tropical**Linear**Spaces*In this section we define local*tropical**linear**spaces**and*prove that they are homeomorphic to Euclidean*space*. ...##
###
Isotropical linear spaces and valuated Delta-matroids

2012
*
Journal of combinatorial theory. Series A
*

In this paper we

doi:10.1016/j.jcta.2011.08.001
fatcat:slzakngcfjckvg6qy2tprk62t4
*tropicalize*this picture,*and*we develop a combinatorial theory of*tropical*Wick vectors*and**tropical**linear**spaces*that are*tropically*isotropic. ... Our theory generalizes several results for*tropical**linear**spaces**and*valuated matroids to the class of Coxeter matroids of type D. ... National Science Foundation (DMS-0456960*and*DMS-0757207). ...##
###
Tropical medians by transportation
[article]

2022
*
arXiv
*
pre-print

This method has several desirable properties; e.g., it is Pareto

arXiv:2205.00036v1
fatcat:fp7z4xtm35genj4lk3nokhcyue
*and*co-Pareto on rooted triplets. ... Fermat-Weber points with respect to an asymmetric*tropical*distance function are studied. It turns out that they correspond to the optimal solutions of a transportation problem. ... The*space*of equidistant trees T n is a max-*tropical**linear**space**and*thus max-*tropically**convex*; see [16, Proposition 10.33]. ...##
###
Computing Convex Hulls in the Affine Building of SL_d
[article]

2018
*
arXiv
*
pre-print

As a consequence, we bound the dimension of the

arXiv:1811.08884v1
fatcat:5kfj5lql2zc2vgk5kyxetpowhu
*tropical*projective*space*needed to realize the*convex*hull as a*tropical*polytope. ... These*convex*hulls describe the relations among a finite collection of invertible matrices over K. ... . , v n ) be a d × n matrix of rank d over K*and*let L be its associated*tropical**linear**space*. ...##
###
Ring of conditions for affine space
[article]

2020
*
arXiv
*
pre-print

The construction of this ring is based on the definition of associated to EAS algebraic subvariety of some multidimensional torus

arXiv:2007.09046v1
fatcat:gsxemxr5xfgcnbg4wgk5oy7u3y
*and*on the applying*tropical*algebraic geometry to this subvariety. ... We consider ES*and*EAS as an analogs of Laurent polynomial*and*of algebraic variety in complex torus (C∖0)^n. ... · s * [4] Let s ′ : V * → E * be an adjoint to s*linear*operator*and*∆ ⊂ V * be a*convex*polyhedron. ...##
###
Multiplicative structure of 2×2 tropical matrices

2011
*
Linear Algebra and its Applications
*

Using ideas from

doi:10.1016/j.laa.2009.12.030
fatcat:mhcg4joxaja7hiy3u6acrxoli4
*tropical*geometry, we give a complete description of Green's relations*and*the idempotents*and*maximal subgroups of this semigroup. (M. Johnson), Mark.Kambites@manchester.ac.uk (M. ... We study the algebraic structure of the semigroup of all 2 × 2*tropical*matrices under multiplication. ... Acknowledgments The authors thank the participants of the Manchester*Tropical*Mathematics Reading Group,*and*the organisers, speakers*and*participants of the First de Brún Workshop on Computational Algebra ...##
###
Tropical Secant Varieties of Linear Spaces

2005
*
Discrete & Computational Geometry
*

In this paper, we investigate

doi:10.1007/s00454-005-1182-2
fatcat:q5cdsf3kifhxdjfiv3nt6j6o3m
*tropical*secant varieties of ordinary*linear**spaces*. ... sets of ordinary toric varieties; we show that their interesting parts are combinatorially isomorphic to a certain natural subcomplex of the complex of regular subdivisions of a corresponding point set,*and*... In particular, theories of*tropical**convexity*[4] ,*tropical*polytopes [5] ,*tropical**linear**spaces*[8] ,*tropical**linear*algebra [3] ,*tropical*geometry [7] ,*and**tropical*algebraic geometry [6] ...##
###
Tropical secant varieties of linear spaces
[article]

2004
*
arXiv
*
pre-print

In this paper, we investigate

arXiv:math/0405115v1
fatcat:4ckvwpspfrhvtbqbsz2rz67koi
*tropical*secant varieties of ordinary*linear**spaces*. ... sets of ordinary toric varieties; we show that their interesting parts are combinatorially isomorphic to a certain natural subcomplex of the complex of regular subdivisions of a corresponding point set,*and*... In particular, theories of*tropical**convexity*[4] ,*tropical*polytopes [5] ,*tropical**linear**spaces*[8] ,*tropical**linear*algebra [3] ,*tropical*geometry [7] ,*and**tropical*algebraic geometry [6] ...
« Previous

*Showing results 1 — 15 out of 9,571 results*