On maximal weakly separated set-systems

Details On maximal weakly separated set-systems On maximal weakly separated set-systems

2009-09-08

arxiv.org/abs/0909.1423v2

J. of Algebraic Combinatorics, 32, 2010, 497-531

Mathematics

Combinatorics

36 pages. This is the final version for J. Algebr. Comb

Scientific paper

For a permutation $\omega\in S_n$, Leclerc and Zelevinsky \cite{LZ} introduced a concept of $\omega$-{\em chamber weakly separated collection} of subsets of $\{1,2,...,n\}$ and conjectured that all inclusion-wise maximal collections of this sort have the same cardinality $\ell(\omega)+n+1$, where $\ell(\omega)$ is the length of $\omega$. We answer affirmatively this conjecture and present a generalization and additional results.

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