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- W2292912795 abstract "In Chapters 2 and 3, we developed the Ehrhart polynomial and Ehrhart series of an integral polytope (mathcal{P}) and realized that the arithmetic information encoded in an Ehrhart polynomial is equivalent to the information encoded in its Ehrhart series. More precisely, when the Ehrhart series is written as a rational function, we introduced the name (h^{{ast}})-polynomial for its numerator: $$displaystyle{mathop{mathrm{Ehr}}nolimits _{mathcal{P}}(z) = 1 +sum _{tgeq 1}L_{mathcal{P}}(t),z^{t} = frac{h_{mathcal{P}}^{{ast}}(z)} {(1 - z)^{dim (mathcal{P})+1}},.}$$Our goal in this chapter is to prove several decomposition formulas for (h_{mathcal{P}}^{{ast}}(z)) based on triangulations of (mathcal{P}). As we will see, these decompositions will involve both arithmetic data from the simplices of the triangulation and combinatorial data from the face structure of the triangulation." @default.
- W2292912795 created "2016-06-24" @default.
- W2292912795 creator A5007719593 @default.
- W2292912795 creator A5046774469 @default.
- W2292912795 date "2015-01-01" @default.
- W2292912795 modified "2023-09-23" @default.
- W2292912795 title "h-Polynomials and h ∗-Polynomials" @default.
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