Abstract
We give a combinatorial formula for the Ehrhart h⁎-vector of the hypersimplex. In particular, we show that hd⁎(Δk,n) is the number of hypersimplicial decorated ordered set partitions of type (k,n) with winding number d, thereby proving a conjecture of N. Early. We do this by proving a more general conjecture of N. Early on the Ehrhart h⁎-vector of a generic cross-section of a hypercube.
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