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Cluster Expansions from Punctured Orbifolds
Esther Banaian, Wonwoo Kang, Elizabeth Kelley +2
We provide multiple combinatorial expansion formulas - in terms of snake graphs, labelled posets, matrices, and -walks - for elements in generalized cluster algebras associated…
Growth of infinite frieze patterns of affine type
Karin Baur, Anna Felikson, Deepanshu Prasad +2
We analyse the growth coefficients of infinite frieze patterns arising from cluster algebras using cluster modular groups and cluster categories. For a fixed cluster category of af…
A mirror deformation of Markov numbers
Léa Bittmann, Perrine Jouteur, Ezgi Kantarcı Oğuz +2
We introduce a deformed squared Markov equation given by . Symmetric solutions of this new equation present a remarka…
Infinite friezes of affine type D
Karin Baur, Léa Bittmann, Emily Gunawan +2
In this article, we study infinite friezes arising from cluster categories of affine type and determine the growth coefficients for these friezes. We prove that for each affine…
Polytopal realizations of non-crystallographic associahedra
Anna Felikson, Pavel Tumarkin, Emine Yildirim
We use the folding technique to show that generalized associahedra for non-simply-laced root systems (including non-crystallographic ones) can be obtained as sections of simply-lac…