The tropical grassmannian
D Speyer, B Sturmfels - 2004 - degruyter.com
… d,n, G00 d,n and G000 d,n when stating our theorems below. In subsequent sections less
precision … By a d-partition we mean an unordered partition of Ωnä into d subsets Ai. Let Lw be a …
precision … By a d-partition we mean an unordered partition of Ωnä into d subsets Ai. Let Lw be a …
Tropical linear spaces
DE Speyer - SIAM Journal on Discrete Mathematics, 2008 - SIAM
… The uniform matroid of rank d on a set S, which we will denote by Uniform(d, S), is the matroid
on S whose bases are all d-element subsets of S. The next two definitions are not standard…
on S whose bases are all d-element subsets of S. The next two definitions are not standard…
Tropical mathematics
D Speyer, B Sturmfels - Mathematics Magazine, 2009 - Taylor & Francis
… D that arises from some biological data then it is reasonable to assume that there exists a tree
metric DT that is close to D… a nearby tree T from the given data D. In what follows we state a …
metric DT that is close to D… a nearby tree T from the given data D. In what follows we state a …
[BOOK][B] Tropical geometry
DE Speyer - 2005 - search.proquest.com
… of d planes in n space. We have a complete and elegant description in the case d = 2 and we
also have a complete description of the case (d… the possible tropicalizations of d planes in n …
also have a complete description of the case (d… the possible tropicalizations of d planes in n …
Positroid varieties: juggling and geometry
… Let S ⊂ Gr(k, n) be the union of all genus-zero stable curves of degree d which intersect
a fixed Schubert variety X and opposite Schubert variety Y . Suppose there is a non-trivial …
a fixed Schubert variety X and opposite Schubert variety Y . Suppose there is a non-trivial …
Computing tropical varieties
T Bogart, AN Jensen, D Speyer, B Sturmfels… - Journal of Symbolic …, 2007 - Elsevier
… In this section we assume that I is a prime ideal of dimension d in C[x1,..., xn]. Then its
tropical variety T (I) is called irreducible. It is a subfan of the Gröbner fan of I and, by the Bieri–…
tropical variety T (I) is called irreducible. It is a subfan of the Gröbner fan of I and, by the Bieri–…
The tropical totally positive Grassmannian
D Speyer, L Williams - Journal of Algebraic Combinatorics, 2005 - Springer
… are closely related to the fans dual to the types D 4 and E 6 associahedra. These results are
… has a natural cluster algebra structure which is of types A n−3 , D 4 , and E 6 for Gr 2,n , Gr 3,…
… has a natural cluster algebra structure which is of types A n−3 , D 4 , and E 6 for Gr 2,n , Gr 3,…
Perfect matchings and the octahedron recurrence
DE Speyer - Journal of Algebraic Combinatorics, 2007 - Springer
… graph and D ⊂ R2 a disc whose boundary meets G only at vertices then G ∩ D naturally
acquires the … 19, we delete edges b and d, reduce the exponents of W and Y by 1 and replace X …
acquires the … 19, we delete edges b and d, reduce the exponents of W and Y by 1 and replace X …
Weak separation and plabic graphs
S Oh, A Postnikov, DE Speyer - Proceedings of the London …, 2015 - academic.oup.com
… We claim that it is impossible that strand |$d$| both passes from |$R$| to |$S_e$| to |$T$| and
from |$T$| to |$S_f$| to |$R$|. The proof is simple: If it did, either its crossings with strand |$…
from |$T$| to |$S_f$| to |$R$|. The proof is simple: If it did, either its crossings with strand |$…
Matching polytopes, toric geometry, and the totally non-negative Grassmannian
A Postnikov, D Speyer, L Williams - Journal of Algebraic Combinatorics, 2009 - Springer
In this paper we use toric geometry to investigate the topology of the totally non-negative part
of the Grassmannian, denoted (Gr k,n ) ≥0 . This is a cell complex whose cells Δ G can be …
of the Grassmannian, denoted (Gr k,n ) ≥0 . This is a cell complex whose cells Δ G can be …