A bivariate generating function for plethysm coefficients with bounded length(λ) is rational; for length 2 an explicit geometric algorithm exists via q-Ehrhart theory, plus linear recursions for the SL2 case.
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Introduces q-, r-, and s-weighted Ehrhart functions, proves rationality and reciprocity results for some, and shows two of them arise as classical Ehrhart rings of weight-lifted polytopes.
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A geometric and generating function approach to plethysm
A bivariate generating function for plethysm coefficients with bounded length(λ) is rational; for length 2 an explicit geometric algorithm exists via q-Ehrhart theory, plus linear recursions for the SL2 case.
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Ehrhart Functions of Weighted Lattice Points
Introduces q-, r-, and s-weighted Ehrhart functions, proves rationality and reciprocity results for some, and shows two of them arise as classical Ehrhart rings of weight-lifted polytopes.