The rank $n$ swapping algebra is the Poisson algebra defined on the ordered pairs of points on a circle using the linking numbers, where a subspace of $(\mathbb{ K}^n \times \mathbb{ K}^{ n*})^r/\operatorname{ GL}(n,\mathbb{ K})$ is its geometric mode. In this paper, we find an injective Poisson homomorphism from the Poisson algebra on Grassmannian $G_{ n,r}$ arising from boundary measurement map to the rank $n$ swapping fraction algebra.
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