Abstract
For a permutation ω∈S 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 ℓ(ω)+n+1, where ℓ(ω) is the length of ω. We answer this conjecture affirmatively and present a generalization and additional results.
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Danilov, V.I., Karzanov, A.V. & Koshevoy, G.A. On maximal weakly separated set-systems. J Algebr Comb 32, 497–531 (2010). https://doi.org/10.1007/s10801-010-0224-x
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DOI: https://doi.org/10.1007/s10801-010-0224-x