The number of complete exceptional sequences for a Dynkin algebra
Volume 133 / 2013
Colloquium Mathematicum 133 (2013), 197-210
MSC: Primary 16G20, 16G60, 05A19, 05E10; Secondary 16D90, 16G70, 16G10.
DOI: 10.4064/cm133-2-6
Abstract
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 $\varDelta $ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type $\varDelta $, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.
