Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.6

The Number of Support-Tilting Modules for a Dynkin Algebra

Mustafa A. A. Obaid, S. Khalid Nauman, Wafaa M. Fakieh, and Claus Michael Ringel
King Abdulaziz University
P. O. Box 80200
Saudi Arabia


The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper exhibits the number of support-tilting modules for any Dynkin algebra. Since the support-tilting modules for a Dynkin algebra of Dynkin type Δ correspond bijectively to the generalized non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of results concerning the generalized non-crossing partitions. In the Dynkin case A, we obtain the Catalan triangle, in the cases B and C the increasing part of the Pascal triangle, and finally in the case D an expansion of the increasing part of the Lucas triangle.

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(Concerned with sequences A007318 A008315 A009766 A029635 A059481 A129869 A241188.)

Received January 5 2015; revised versions received September 7 2015; September 18 2015. Published in Journal of Integer Sequences, September 24 2015.

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