Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of complete exceptional sequences for a Dynkin algebra   We consider Dynkin algebras, these are the hereditary artin algebras of
finite representation type. The indecomposable modules for a Dynkin algebra
correspond bijectively to the positive roots of a Dynkin diagram. Given a
Dynkin algebra with n simple modules, a complete exceptional sequence is a
sequence M_1,..., M_n of indecomposable modules such that Hom(M_i,M_j) = 0 =
Ext(M_i,M_j) for i > j. The aim of this paper is to determine the number of
complete exceptional sequences for any Dynkin algebra.
  There are direct connections between the representation theory of a Dynkin
algebra A and the lattice L of non-crossing partitions of the same Dynkin type:
As Ingalls and Thomas have shown, the lattice of the thick subcategories of mod
A can be identified with L. Hubery and Krause have pointed out that this
identification provides a bijection between the complete exceptional sequences
for A and the maximal chains in L. Thus, our calculations may also be
considered as a categorification of results concerning non-crossing partitions.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: econ