V. I. Danilov, A. V. Karzanov, G. A. Koshevoy, “Separated set-systems and their geometric models”, Uspekhi Mat. Nauk, 2010, Volume 65, Issue 4(394),Pages <nobr>67

This article is cited in 8 papers

Separated set-systems and their geometric models

V. I. Danilov^a, A. V. Karzanov^b, G. A. Koshevoy^a

^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.

UDC: 519.1+512.81

MSC: Primary 05B45, 05C75, 06A07; Secondary 15A48, 17B37

Received: 06.12.2009

DOI: 10.4213/rm9364