11 citations · 42 across the 22 of their papers we have counts for
4 papers · 1 filter
Splitting loops and necklaces: Variants of the square peg problem
Jai Aslam, Shujian Chen, Florian Frick +3
Toeplitz conjectured that any simple planar loop inscribes a square. Here we prove variants of Toeplitz' square peg problem. We prove Hadwiger's 1971 conjecture that any simple loo…
Independence Posets
Hugh Thomas, Nathan Williams
Let be an acylic directed graph. For each vertex , we define an involution on the independent sets of . We call these involutions flips, and use them to define a ne…
Torsion pairs for quivers and the Weyl groups
Yuya Mizuno, Hugh Thomas
We give an interpretation of the map defined by Reading, which is a map from the elements of a Coxeter group to the -sortable elements, in terms of the representation theo…
Coxeter groups and quiver representations
Hugh Thomas
In this expository note, I showcase the relevance of Coxeter groups to quiver representations. I discuss (1) real and imaginary roots, (2) reflection functors, and (3) torsion free…