Geodesic
Combinatorics of exceptional sequences in type A
Alexander Garver1 ; Kiyoshi Igusa2 ; Jacob P. Matherne3 ; Jonah Ostroff4
1Université du Québec à Montréal
2Brandeis University
3Institute for Advanced Study
4University of Washington
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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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.
DOI : 10.37236/6251
Classification : 16G20, 05E10, 13F60
Mots-clés : strand diagrams, \(\mathbf c\)-matrices, quivers

Alexander Garver  1   ; Kiyoshi Igusa  2   ; Jacob P. Matherne  3   ; Jonah Ostroff  4

1 Université du Québec à Montréal
2 Brandeis University
3 Institute for Advanced Study
4 University of Washington 
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     title = {Combinatorics of exceptional sequences in type {A}},
     journal = {The electronic journal of combinatorics},
     year = {2019},
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     number = {1},
     doi = {10.37236/6251},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/6251/}
}
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Alexander Garver; Kiyoshi Igusa; Jacob P. Matherne; Jonah Ostroff. Combinatorics of exceptional sequences in type A. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/6251

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