Combinatorics of Exceptional Sequences in Type A

  • Alexander Garver
  • Kiyoshi Igusa
  • Jacob P. Matherne
  • Jonah Ostroff


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 $c$-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. 

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