A natural piecewise Euclidean bi-simplicial cell structure exists for the space of n-element multisets in a Euclidean rectangle, with noted connections to complex polynomial spaces and permutahedra.
Wachs,Poset topology: tools and applications, Geometric combinatorics, IAS/Park City Math
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The Geometry of Rectangular Multisets
A natural piecewise Euclidean bi-simplicial cell structure exists for the space of n-element multisets in a Euclidean rectangle, with noted connections to complex polynomial spaces and permutahedra.