4 papers
Building maximal green sequences via component preserving mutations
Eric Bucher, John Machacek, Evan Runburg +2
We introduce a new method for producing both maximal green and reddening sequences of quivers. The method, called component preserving mutations, generalizes the notion of direct s…
Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions
Eric Bucher, Chris Eppolito, Jaiung Jun +1
In this paper, we give a cancellation-free antipode formula for the matroid-minor Hopf algebra. We then explore applications of this formula. For example, the cancellation-free for…
Reddening Sequences for Banff Quivers and the Class
Eric Bucher, John Machacek
We show that a reddening sequence exists for any quiver which is Banff. Our proof is combinatorial and relies on the triangular extension construction for quivers. The other facts…
Upper cluster algebras and choice of ground ring
Eric Bucher, John Machacek, Michael Shapiro
We initiate a study of the dependence on the choice of ground ring on the question of whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is…