Local h^*-polynomials for one-row Hermite normal form simplices
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The local $h^*$-polynomial of a lattice polytope is an important invariant arising in Ehrhart theory. Our focus is on lattice simplices presented in Hermite normal form with a single non-trivial row. We prove that when the off-diagonal entries are fixed, the distribution of coefficients for the local $h^*$-polynomial of these simplices has a limit as the normalized volume goes to infinity. Further, this limiting distribution is determined by the coefficients for a particular choice of normalized volume. We also provide an analysis of two specific families of such simplices to illustrate and motivate our main result.
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Cited by 2 Pith papers
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Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern
Explicit construction of d-dimensional integral polytopes realizing arbitrary sign patterns in Ehrhart polynomial coefficients via tunable simplices and Cartesian products with the Reeve tetrahedron.
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Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern
Explicit constructions of d-dimensional integral polytopes realizing any given sign pattern in Ehrhart polynomial coefficients via simplices S_d(m) and Cartesian products with the Reeve tetrahedron.
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