10 citations · 37 across the 9 of their papers we have counts for
10 papers
Reddening sequences and mutation of infinite quivers
Eric Bucher, Elizabeth Howard
Cluster algebras, introduced by Fomin and Zelevinsky through the process of quiver mutation, have become central objects in modern algebra and geometry, linking combinatorial const…
Red sizes of quivers
Eric Bucher, John Machacek
In this article, we will expand on the notions of maximal green and reddening sequences for quivers associated to cluster algebras. The existence of these sequences has been studie…
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…