Nathan Williams

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Each positive rational number x > 0 can be written uniquely as x = a/(b − a) for coprime positive integers 0 < a < b. We will identify x with the pair (a, b). In this paper we define for each positive rational x > 0 a simplicial complex Ass(x) = Ass(a, b) called the rational associahedron. It is a pure simplicial complex of dimension a − 2, and its maximal(More)
We present an equivariant bijection between two actions—promotion and rowmotion—on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and certain cases of recent work of D. Armstrong, C. Stump, and H. Thomas on noncrossing and nonnesting(More)
W e examine, in a strategic setting, the broad issue of how retail channel structures—retail monopoly versus retail duopoly—impact a manufacturer's optimal new product design, both in terms of engineering design specifications as well as manufacturer and retailer profits. Our strategic framework enables manufacturers in specific contexts to anticipate the(More)
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