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Russian Mathematical Surveys, 2010, Volume 65, Issue 4, Pages 659–740
DOI: https://doi.org/10.1070/RM2010v065n04ABEH004692 (Mi rm9364) 		 
This article is cited in 8 scientific papers (total in 8 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
English version PDF (1313 kB) Citations (8)
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DOI: https://doi.org/10.1070/RM2010v065n04ABEH004692
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.
Received: 06.12.2009
Russian version:
Uspekhi Matematicheskikh Nauk, 2010, Volume 65, Issue 4(394), Pages 67–152
DOI: https://doi.org/10.4213/rm9364
Bibliographic databases:
Document Type: Article
UDC: 519.1+512.81
MSC: Primary 05B45, 05C75, 06A07; Secondary 15A48, 17B37
Language: English
Original paper language: Russian
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 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:594
    English version PDF:47
    References:93
    First page:30
     
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