Geodesic
The number of support-tilting modules for a Dynkin algebra
Journal of integer sequences, Tome 18 (2015) no. 10
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 $\Delta $ correspond bijectively to the generalized non-crossing partitions of type $\Delta $, 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.
Classification : 05E10
Keywords: Dynkin algebra, Dynkin diagram, tilting module, support-tilting module, lattice of non-crossing partitions, cluster combinatorics, generalized Catalan number, Catalan triangle, Pascal triangle, Lucas triangle, categorification 
@article{JIS_2015__18_10_a1,
     author = {Obaid,  Mustafa A.A. and Nauman,  S.Khalid and Fakieh,  Wafaa M. and Ringel,  Claus Michael},
     title = {The number of support-tilting modules for a {Dynkin} algebra},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {10},
     zbl = {1328.05198},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a1/}
}
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Obaid,  Mustafa A.A.; Nauman,  S.Khalid; Fakieh,  Wafaa M.; Ringel,  Claus Michael. The number of support-tilting modules for a Dynkin algebra. Journal of integer sequences, Tome 18 (2015) no. 10. http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a1/