Given a tree embedded in a disk, we define two lattices the oriented flip graph of noncrossing arcs and the lattice of noncrossing tree partitions. When the interior vertices of the tree have degreeâ€¦ (More)

The exchange graph of a quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. The exchange graph admits a natural acyclic orientation called the oriented exchangeâ€¦ (More)

Given a tree embedded in a disk, we introduce a simplicial complex of noncrossing geodesics supported by the tree, which we call the noncrossing complex. The facets of the noncrossing complex haveâ€¦ (More)

Figure: Type IV quivers Mutation type Ä‚ A and Type IV quivers have the same underlying graphs. Corollary (G.â€“McConvilleâ€“Serhiyenko 2017) i) `min â€œ n ` |t3-cycles in Ä‚ Qu| ( Q is Type I or type Ä‚ Anâ€¦ (More)

Consider 2n points on the unit circle and a reference dissection Dâ—¦ of the convex hull of the odd points. The accordion complex of Dâ—¦ is the simplicial complex of non-crossing subsets of theâ€¦ (More)

We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for theâ€¦ (More)

Purpose Mind/body practices that elicit the relaxation response (RR) have been used for health purposes for thousands of years, but mechanisms of action are not clearly understood. Our research teamâ€¦ (More)

We investigate a variant of the chip-firing process on the infinite path graph Z: rather than treating the chips as indistinguishable, we label them with positive integers. To fire an unstableâ€¦ (More)