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Combinatorics of exceptional sequences in type A. (English) Zbl 1456.16009

Summary: Exceptional sequences are certain sequences of quiver representations. We introduce a class of objects called strand diagrams and use these to classify exceptional sequences of representations of a quiver whose underlying graph is a type \(\mathbb{A}_n\) Dynkin diagram. We also use variations of these objects to classify \(\mathbf c\)-matrices of such quivers, to interpret exceptional sequences as linear extensions of explicitly constructed posets, and to give a simple bijection between exceptional sequences and certain saturated chains in the lattice of noncrossing partitions.

MSC:

16G20 Representations of quivers and partially ordered sets
05E10 Combinatorial aspects of representation theory
13F60 Cluster algebras
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References:

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