Results 61 to 70 of about 5,701 (91)
Broken lines and compatible pairs for rank 2 quantum cluster algebras
There have been several combinatorial constructions of universally positive bases in cluster algebras, and these same combinatorial objects play a crucial role in the known proofs of the famous positivity conjecture for cluster algebras. The greedy basis
Burcroff, Amanda, Lee, Kyungyong
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Skew-group $A_{\infty}$-categories as Fukaya categories of orbifolds
We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the role of the ...
Amiot, Claire, Plamondon, Pierre-Guy
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Positivity in Cluster Algebras and Their Generalizations [PDF]
The theory of bf cluster algebras gives us a combinatorial framework for understanding the previously opaque nature of certain algebras. Each cluster algebra is generated by its cluster variables, which can be obtained via the recursive process of ...
Burcroff, Amanda
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Friezes over $\mathbb Z[\sqrt{2}]$
A frieze on a polygon is a map from the diagonals of the polygon to an integral domain which respects the Ptolemy relation. Conway and Coxeter previously studied positive friezes over $\mathbb{Z}$ and showed that they are in bijection with triangulations
Banaian, Esther +4 more
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Maximal almost rigid modules over gentle algebras
We study maximal almost rigid modules over a gentle algebra $A$. We prove that the number of indecomposable direct summands of every maximal almost rigid $A$-module is equal to the sum of the number of vertices and the number of arrows of the Gabriel ...
Barnard, Emily +3 more
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The effect of case-based mobile virtual patient application on students' academic achievement in clinical reasoning skills. [PDF]
Med Educ OnlineÇetinkaya L +3 more
europepmc +1 more source
Metric completions of discrete cluster categories
Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, for a
Cummings, Charley, Gratz, Sira
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Dimer face polynomials in knot theory and cluster algebras
The set of perfect matchings of a connected bipartite plane graph $G$ has the structure of a distributive lattice, as shown by Propp, where the partial order is induced by the height of a matching.
Musiker, Gregg +3 more
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