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Akihiro Higashitani:Universal inequalities for h*-vectors of lattice polytopes

Time: Wed 2021-09-15 10.15 - 11.15

Location: Zoom meeting ID: 654 5562 3260

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Abstract: A characterization problem for \(h^*\)-polynomials of lattice polytopes is one of the most well-studied topics in Ehrhart theory. It was proved in 2018 that for the \(h^*\)-polynomial \(h_0^*+h_1^*t+h_2^*t^2+\dots\) of a lattice polytope, if we assume \(h_3^*=0\), then the first three terms \(h_0^*+h_1^*t+h_2^*t^2\) satisfy the same inequalities as ones for the \(h^*\)-polynomials of lattice polytopes with degree at most 2, which are so-called Scott's inequality. Since the assumption \(h_3^*=0\) is independent of both dimension and degree of polytopes, we call such inequalities universal.
In this talk, towards finding a new universal inequality, we discuss whether the first \(k\) terms of the \(h^*\)-polynomial of some lattice polytope
can be the \(h^*\)-polynomial of other lattice polytope under the assumption that some of \(h^*\)'s vanish.

Zoom meeting ID: 654 5562 3260

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