Fetching the paper…
Reading the bibliography…
We prove that three spaces of importance in topological combinatorics are homeomorphic to closed balls: the totally nonnegative Grassmannian, the compactification of the space of electrical networks, and the cyclically symmetric amplituhedron.
The Bruhat order of the symmetric group is lexicographically shellable
Paul H. Edelman · 1981
Earlier work this paper cites.
Posets, regular CW complexes and Bruhat order
A. Björner · 1984
Earlier work this paper cites.
Totally positive matrices and cyclic polytopes
Bernd Sturmfels · 1988
Earlier work this paper cites.
Total positivity in reductive groups
G. Lusztig · 1994
Earlier work this paper cites.
Réseaux électriques planaires. II
Yves Colin de Verdière, Isidoro Gitler, and Dirk Vertigan · 1996
Earlier work this paper cites.
Circular planar graphs and resistor networks
E. B. Curtis, D. Ingerman, and J. A. Morrow · 1998
Earlier work this paper cites.
Introduction to total positivity
George Lusztig · 1998
Earlier work this paper cites.
An algebraic cell decomposition of the nonnegative part of a flag variety
Konstanze Rietsch · 1999
Earlier work this paper cites.
Stratified spaces formed by totally positive varieties
Sergey Fomin and Michael Shapiro · 2000
Earlier work this paper cites.
Control sets and total positivity
Víctor Ayala, Wolfgang Kliemann, and Luiz A. B. San Martin · 2004
Earlier work this paper cites.
Closure relations for totally nonnegative cells in G / P G/P
K. Rietsch · 2006
Earlier work this paper cites.
Total positivity, Grassmannians, and networks
Alexander Postnikov · 2007
Earlier work this paper cites.
Shelling totally nonnegative flag varieties
Lauren K. Williams · 2007
Cited alongside, same era.
A mirror symmetric construction of q H T ∗ ( G / P ) ( q ) qH^{\ast}_{T}(G/P)_{(q)}
Konstanze Rietsch · 2008
Cited alongside, same era.
Matching polytopes, toric geometry, and the totally non-negative Grassmannian
Alexander Postnikov, David Speyer, and Lauren Williams · 2009
Cited alongside, same era.
Discrete Morse theory for totally non-negative flag varieties
Konstanze Rietsch and Lauren Williams · 2010
Cited alongside, same era.
Combinatorial formulas for Le-coordinates in a totally nonnegative Grassmannian
Kelli Talaska · 2011
Cited alongside, same era.
The Laplacian on planar graphs and graphs on surfaces
R. Kenyon · 2012
Cited alongside, same era.
Totally nonnegative Grassmannian and Grassmann polytopes
Thomas Lam · 2016
Later among the works it cites.
Positive geometries and canonical forms
Nima Arkani-Hamed, Yuntao Bai, and Thomas Lam · 2017
Closest in time.
Positively oriented matroids are realizable
Federico Ardila, Felipe Rincón, and Lauren Williams · 2017
Closest in time.
Unwinding the amplituhedron in binary
Nima Arkani-Hamed, Hugh Thomas, and Jaroslav Trnka · 2018
Closest in time.
Electroid varieties and a compactification of the space of electrical networks
Thomas Lam · 2018
Closest in time.
Regularity theorem for totally nonnegative flag varieties
Pavel Galashin, Steven N. Karp, and Thomas Lam · 2019
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Total positivity in loop groups, I: Whirls and curls
Thomas Lam and Pavlo Pylyavskyy · 2012
Cited alongside, same era.
The amplituhedron
Nima Arkani-Hamed and Jaroslav Trnka · 2014
Cited alongside, same era.
Regular cell complexes in total positivity
Patricia Hersh · 2014
Cited alongside, same era.
The uncrossing partial order on matchings is Eulerian
Thomas Lam · 2015
Cited alongside, same era.
Grassmannian Geometry of Scattering Amplitudes
Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, and Jaroslav Trnka · 2016
Cited alongside, same era.
Note on a theorem of Prof. Cayley’s
R. F. Scott
Cited in the paper.
The totally nonnegative part of G / P G/P is a ball
Pavel Galashin, Steven N. Karp, and Thomas Lam · 2019
Closest in time.
Moment curves and cyclic symmetry for positive Grassmannians
Steven N. Karp · 2019
Closest in time.
The m = 1 m=1 amplituhedron and cyclic hyperplane arrangements
Steven N. Karp and Lauren K. Williams · 2019
Closest in time.
The B B -model connection and mirror symmetry for Grassmannians
R. J. Marsh and K. Rietsch · 2020
Closest in time.
Shellability of face posets of electrical networks and the CW poset property
Patricia Hersh and Richard Kenyon · 2021
Closest in time.