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pro vyhledávání: '"Bucher, Eric"'
Autor:
Bucher, Eric, Machacek, John
Publikováno v:
Arnold Mathematical Journal (2023)
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 studied for a variety of applications related to Fomin and Zelevinsky's clus
Externí odkaz:
http://arxiv.org/abs/2204.03212
Publikováno v:
Ars Math. Contemp. 19 (2020), no. 2, 249--275
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 sums of quivers and can be used as a tool to both recover known reddeni
Externí odkaz:
http://arxiv.org/abs/1902.02262
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 formula expresses the antipode of uniform matroids as a sum over certain
Externí odkaz:
http://arxiv.org/abs/1811.01687
Autor:
Bucher, Eric
Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior
Externí odkaz:
http://etd.lsu.edu/docs/available/etd-07052016-180347/
Autor:
Bucher, Eric, Machacek, John
Publikováno v:
SIGMA 16 (2020), 049, 11 pages
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 needed are that the existence of a reddening sequence is mutation inva
Externí odkaz:
http://arxiv.org/abs/1807.03359
Publikováno v:
Sci. China Math. 62 (2019), no. 7, 1257-1266
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 equality of the cluster algebra and upper cluster algebra is given by
Externí odkaz:
http://arxiv.org/abs/1802.04835
Autor:
Bucher, Eric, Matherne, Jacob P.
In this paper, we give a cancellation-free antipode formula (for uniform matroids) for the restriction-contraction matroid Hopf algebra, using the technique of splitting and merging via a sign-reversing involution. The cancellation-free formula expre
Externí odkaz:
http://arxiv.org/abs/1612.04343
Autor:
Bucher, Eric, Pindra, Stephanie
Publikováno v:
YC Young Children, 2020 May 01. 75(2), 16-23.
Externí odkaz:
https://www.jstor.org/stable/26979141
Autor:
Bucher, Eric, Yakimov, Milen
We present an effective method for recovering the topology of a bordered oriented surface with marked points from its cluster algebra. The information is extracted from the maximal triangulations of the surface, those that have exchange quivers with
Externí odkaz:
http://arxiv.org/abs/1607.02131
Autor:
Bucher, Eric, Mills, Matthew R.
It is well known that any triangulation of a marked surface produces a quiver. In this paper we will provide a triangulation for orientable surfaces of genus $n$ with an arbitrary number interior marked points (called punctures) whose corresponding q
Externí odkaz:
http://arxiv.org/abs/1503.06207