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Journal of Algebraic Combinatorics

, Volume 32, Issue 4, pp 497–531 | Cite as

On maximal weakly separated set-systems

  • Vladimir I. Danilov
  • Alexander V. Karzanov
  • Gleb A. Koshevoy
Article

Abstract

For a permutation ωS n , Leclerc and Zelevinsky in Am. Math. Soc. Transl., Ser. 2 181, 85–108 (1998) introduced the concept of an ω-chamber weakly separated collection of subsets of {1,2,…,n} and conjectured that all inclusionwise maximal collections of this sort have the same cardinality (ω)+n+1, where (ω) is the length of ω. We answer this conjecture affirmatively and present a generalization and additional results.

Keywords

Weakly separated sets Rhombus tiling Generalized tiling Weak Bruhat order Cluster algebras 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Vladimir I. Danilov
    • 1
  • Alexander V. Karzanov
    • 2
  • Gleb A. Koshevoy
    • 1
  1. 1.Central Institute of Economics and Mathematics of the RASMoscowRussia
  2. 2.Institute for System Analysis of the RASMoscowRussia

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