AFFINE BUILDINGS AND TROPICAL CONVEXITY

By Michael Joswig, Bernd Sturmfels, Josephine Yu. Albanian Journal of Mathematics, 2007

71 citations recorded by the source corpus.

The notion of convexity in tropical geometry is closely related to notions of convexity in the theory of affine buildings. We explore this relationship from a combinatorial and computational perspective. Our results include a convex hull algorithm for the Bruhat--Tits building of SL$_d(K)$ and techniques for computing with apartments and membranes. 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 problems in other fields of mathematics.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/79b8ace53e9f8d51cad9641235f531f78ac37a2d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Marianne Akian
2. Stephane Gaubert
3. Katja Kulas
4. Michael Joswig

In Computational Theory and Mathematics

1. Marianne Akian
2. Stephane Gaubert
3. Michael Joswig
4. Katja Kulas
5. Ricardo D. Katz
6. Peter Butkovic
7. Grigori L. Litvinov

In Discrete Mathematics and Combinatorics

1. Katja Kulas
2. Stephane Gaubert
3. Michael Joswig
4. Roland R. Ramsahai
5. Stefan Forcey
6. N. Fakhruddin

Citations in the corpus

• Best approximation in max-plus semimodules☆ (2010, background): “Then (see [8, 13, 16]) for any x ∈ Rmax, PV (x) is a best approximation of x in V (such a best approximation is not necessarily unique), that is,”
• Tropical and Ordinary Convexity Combined (2008, background): “Note that TA was called “tropical projective space” in [8], [14], [9], and [15].”