Signature matrices of membranes

Felix Lotter, Leonard Schmitz
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Abstract

We prove that, unlike in the case of paths, the signature matrix of a membrane does not satisfy any algebraic relations. We derive novel closed-form expressions for the signatures of polynomial membranes and piecewise bilinear interpolations for arbitrary $2$-parameter data in $d$-dimensional space. We show that these two families of membranes admit the same set of signature matrices and scrutinize the corresponding affine variety.
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膜的特征矩阵
我们证明,与路径的情况不同,膜的签名矩阵不满足任何代数关系。我们为多项式膜和片断双线性插值的签名推导出了新的闭公式表达式,适用于 $d$ 维空间中任意 $2$ 参数的数据。我们发现这两个膜家族允许相同的签名矩阵集,并仔细研究了相应的仿射变种。
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New characterization of $(b,c)$-inverses through polarity Relative torsionfreeness and Frobenius extensions Signature matrices of membranes On denominator conjecture for cluster algebras of finite type Noetherianity of Diagram Algebras
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