Alexander Garver ; Jacob P. Matherne - A combinatorial model for exceptional sequences in type A

dmtcs:2513 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2513
A combinatorial model for exceptional sequences in type A

Authors: Alexander Garver 1; Jacob P. Matherne 2

  • 1 School of Mathematics
  • 2 Department of Mathematics Louisiana State University

Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya’s work) to classify exceptional sequences of representations of $Q$, the linearly ordered quiver with $n$ vertices. We also show how to use variations of this model to classify $c$-matrices of $Q$, to interpret exceptional sequences as linear extensions, and to give a simple bijection between exceptional sequences and certain chains in the lattice of noncrossing partitions. In the case of $c$-matrices, we also give an interpretation of $c$-matrix mutation in terms of our noncrossing trees with directed edges.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: quiver mutation,exceptional sequences,$c$-matrices,linear extensions,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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Source : ScholeXplorer IsRelatedTo ARXIV 1506.08927
Source : ScholeXplorer IsRelatedTo DOI 10.37236/6251
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1506.08927
  • 10.48550/arxiv.1506.08927
  • 10.37236/6251
  • 10.37236/6251
  • 1506.08927
Combinatorics of exceptional sequences in type A

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