The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Δ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-6,
author = {Mustafa Obaid and Khalid Nauman and Wafa S. M. Al-Shammakh and Wafaa Fakieh and Claus Michael Ringel},
title = {The number of complete exceptional sequences for a Dynkin algebra},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {197-210},
zbl = {1286.16016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-6}
}
Mustafa Obaid; Khalid Nauman; Wafa S. M. Al-Shammakh; Wafaa Fakieh; Claus Michael Ringel. The number of complete exceptional sequences for a Dynkin algebra. Colloquium Mathematicae, Tome 131 (2013) pp. 197-210. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-6/