Geodesic
On maximal weakly separated set-systems
Journal of Algebraic Combinatorics, Tome 32 (2010) no. 4, pp. 497-531.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For a permutation $\omega \in S _{ n }$, Leclerc and Zelevinsky in Am. Math. Soc. Transl., Ser. 2 181, 85-108 ( 1998) introduced the concept of an $\omega $- chamber weakly separated collection of subsets of ${1,2,\cdots , n}$ and conjectured that all inclusionwise maximal collections of this sort have the same cardinality $\ell ( \omega )+ n+1$, where $\ell ( \omega )$ is the length of $\omega $. We answer this conjecture affirmatively and present a generalization and additional results.
Keywords: keywords weakly separated sets, rhombus tiling, generalized tiling, weak Bruhat order, cluster algebras 
@article{JAC_2010__32_4_a4,
     author = {Danilov, Vladimir I. and Karzanov, Alexander V. and Koshevoy, Gleb A.},
     title = {On maximal weakly separated set-systems},
     journal = {Journal of Algebraic Combinatorics},
     pages = {497--531},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__32_4_a4/}
}
TY  - JOUR
AU  - Danilov, Vladimir I.
AU  - Karzanov, Alexander V.
AU  - Koshevoy, Gleb A.
TI  - On maximal weakly separated set-systems
JO  - Journal of Algebraic Combinatorics
PY  - 2010
SP  - 497
EP  - 531
VL  - 32
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2010__32_4_a4/
LA  - en
ID  - JAC_2010__32_4_a4
ER  - 
%0 Journal Article
%A Danilov, Vladimir I.
%A Karzanov, Alexander V.
%A Koshevoy, Gleb A.
%T On maximal weakly separated set-systems
%J Journal of Algebraic Combinatorics
%D 2010
%P 497-531
%V 32
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2010__32_4_a4/
%G en
%F JAC_2010__32_4_a4
Danilov, Vladimir I.; Karzanov, Alexander V.; Koshevoy, Gleb A. On maximal weakly separated set-systems. Journal of Algebraic Combinatorics, Tome 32 (2010) no. 4, pp. 497-531. http://geodesic.mathdoc.fr/item/JAC_2010__32_4_a4/