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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 4(394), Pages 67–152 (Mi umn9364)  

This article is cited in 3 scientific papers (total in 3 papers)

Separated set-systems and their geometric models

V. I. Danilova, A. V. Karzanovb, G. A. Koshevoya

a Central Economics and Mathematics Institute, RAS
b Institute of Systems Analysis, Russian Academy of Sciences

Abstract: This paper discusses strongly and weakly separated set-systems as well as rhombus tilings and wiring diagrams which are used to produce such systems. In particular, the Leclerc–Zelevinsky conjectures concerning weakly separated systems are proved.
Bibliography: 54 titles.

Keywords: Plücker relations, Laurent phenomenon, wiring, total positivity, rhombus tiling, Bruhat order.

DOI: https://doi.org/10.4213/rm9364

Full text: PDF file (1506 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2010, 65:4, 659–740

Bibliographic databases:

Document Type: Article
UDC: 519.1+512.81
MSC: Primary 05B45, 05C75, 06A07; Secondary 15A48, 17B37
Received: 06.12.2009

Citation: V. I. Danilov, A. V. Karzanov, G. A. Koshevoy, “Separated set-systems and their geometric models”, Uspekhi Mat. Nauk, 65:4(394) (2010), 67–152; Russian Math. Surveys, 65:4 (2010), 659–740

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Fomin S., Grigoriev D., Koshevoy G., “Subtraction-Free Complexity, Cluster Transformations, and Spanning Trees”, Found. Comput. Math., 16:1 (2016), 1–31  crossref  mathscinet  zmath  isi  elib  scopus
    2. Santos F., Stump Ch., Welker V., “Noncrossing Sets and a Grassmann Associahedron”, Forum Math. Sigma, 5 (2017), e5  crossref  mathscinet  zmath  isi
    3. Agaltsov A.D., Molchanov E.G., Shananin A.A., “Inverse Problems in Models of Resource Distribution”, J. Geom. Anal., 28:1 (2018), 726–765  crossref  mathscinet  zmath  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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