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We associate a dimer algebra A to a Postnikov diagram D (in a disk) corresponding to a cluster of minors in the cluster structure of the Grassmannian Gr(k,n).
Translated from the Japanese by M. Reid
BibliographyH. Matsumura, Commutative ring theory, · 1986
Earlier work this paper cites.
BibliographyM. Ciucu, A complementation theorem for perfect matchings of graphs having a cellular completion, J. Combin. Theory Ser. A
1998
Earlier work this paper cites.
BibliographyB. Leclerc, A. Zelevinsky, Quasicommuting families of quantum Plücker coordinates, in: Kirillov’s seminar on representation theory, Amer. Math. Soc. Transl. Ser. 2
1998
Earlier work this paper cites.
BibliographyR.W. Kenyon, J.G. Propp, D.B. Wilson, Trees and matchings, Electron. J. Combin
2000
Earlier work this paper cites.
BibliographyS. Fomin, A. Zelevinsky, Cluster algebras. I. Foundations, J. Amer. Math. Soc
2002
Earlier work this paper cites.
BibliographyS. Franco, A. Hanany, K.D. Kennaway, D. Vegh, B. Wecht, Brane Dimers and Quiver Gauge Theories, JHEP
2006
Earlier work this paper cites.
BibliographyA. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math/0609764v1 [math.CO] Sep 2006
2006
Earlier work this paper cites.
BibliographyJ.S. Scott, Grassmannians and cluster algebras, Proc. London Math. Soc. (3)
2006
Earlier work this paper cites.
BibliographyV. Ginzburg, Calabi-Yau algebras, arXiv:math/0612139v3 [math.AG] Jan 2007
2007
Earlier work this paper cites.
BibliographyA. Hanany, D. Vegh, Quivers, tilings, branes and rhombi, JHEP
2007
Cited alongside, same era.
BibliographyH. Derksen, J. Weyman, A. Zelevinsky, Quivers with potentials and their representations. I. Mutations., Selecta Math. (N.S.)
2008
Cited alongside, same era.
BibliographyS. Fomin, M. Shapiro, D. Thurston, Cluster algebras and triangulated surfaces. I. Cluster complexes., Acta Math
2008
Cited alongside, same era.
BibliographyC. Geiss, B. Leclerc, J. Schröer, Partial flag varieties and preprojective algebras, Ann. Inst. Fourier
2008
Cited alongside, same era.
BibliographyD.R. Gulotta, Properly ordered dimers, R-charges, and an efficient inverse algorithm, JHEP
2008
Cited alongside, same era.
BibliographyR. Bocklandt, Consistency conditions for dimer models, Glasg. Math. J
2012
Later among the works it cites.
BibliographyN. Broomhead, Dimer models and Calabi-Yau algebras, Mem. Amer. Math. Soc
2012
Later among the works it cites.
BibliographyS. Franco, Bipartite Field Theories: from D-Brane Probes to Scattering Amplitudes, JHEP
2012
Later among the works it cites.
BibliographyR. Bocklandt, Calabi-Yau algebras and weighted quiver polyhedra, Math. Z
2013
Closest in time.
BibliographyA.B. Goncharov, R. Kenyon, Dimers and cluster integrable systems, Ann. Sci. Éc. Norm. Sup. (4)
2013
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2009
Cited alongside, same era.
BibliographyV.I. Danilov, A.V. Karzanov, G.A. Koshevoy, On maximal weakly separated set-systems, J. Algebraic Combin
2010
Cited alongside, same era.
BibliographyA.B. Buan, O. Iyama, I. Reiten, D. Smith, Mutation of cluster-tilting objects and potentials, Amer. J. Math
2011
Cited alongside, same era.
BibliographyB. Davison, Consistency conditions for brane tilings, J. Algebra
2011
Cited alongside, same era.
BibliographyB. Jensen, A. King, X. Su, A categorification of Grassmannian Cluster Algebras, arXiv:1309.7301v2 [math.RT] Dec 2014 · 2014
Closest in time.
BibliographyS. Oh, A. Postnikov, D.E. Speyer, Weak Separation and Plabic Graphs, Proc. Lond. Math. Soc. (3)
2015
Closest in time.
BibliographyL. Demonet, X. Luo, Ice quivers with potentials associated with triangulations and Cohen-Macaulay modules over orders, Trans. Amer. Math. Soc
2016
Closest in time.
BibliographyR.J. Marsh, J.S. Scott, Twists of Plücker coordinates as dimer partition functions, Comm. Math. Phys
2016
Closest in time.