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Award ID contains: 1854162

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  1. ; ; (, Journal of Geometry and Physics)
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  2. ; (, The Electronic Journal of Combinatorics)
    We define a combinatorial model for $$F$$-polynomials and $$g$$-vectors for type $$D_n$$ cluster algebras where the associated quiver is acyclic. Our model utilizes a combination of dimer configurations and double dimer configurations which we refer to as mixed dimer configurations. In particular, we give a graph theoretic recipe that describes which monomials appear in such $$F$$-polynomials, as well as a graph theoretic way to determine the coefficients of each of these monomials. In addition, we prove that a weighting on our mixed dimer configuration model yields the associated $$g$$-vector. To prove this formula, we use a combinatorial formula due to Thao Tran (arXiv:0911.4462, 2009) and provide explicit bijections between her combinatorial model and our own. 
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  3. ; ; ; ; ; (, Physical Review D)
    null (Ed.)
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