Geodesic
The number of support-tilting modules for a Dynkin algebra
Journal of integer sequences, Tome 18 (2015) no. 10
Zbl arXiv
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 
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/
@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/}
}
TY  - JOUR
AU  - Obaid,  Mustafa A.A.
AU  - Nauman,  S.Khalid
AU  - Fakieh,  Wafaa M.
AU  - Ringel,  Claus Michael
TI  - The number of support-tilting modules for a Dynkin algebra
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a1/
LA  - en
ID  - JIS_2015__18_10_a1
ER  - 
%0 Journal Article
%A Obaid,  Mustafa A.A.
%A Nauman,  S.Khalid
%A Fakieh,  Wafaa M.
%A Ringel,  Claus Michael
%T The number of support-tilting modules for a Dynkin algebra
%J Journal of integer sequences
%D 2015
%V 18
%N 10
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a1/
%G en
%F JIS_2015__18_10_a1