An Ehrhart series formula for reflexive polytopes. (English) Zbl 1109.52011
Summary: It is well known that for \(P\) and \(Q\) lattice polytopes, the Ehrhart polynomial of \(P \times Q\) satisfies \(L_{P \times Q}(t)=L_P(t)L_Q(t)\).
We show that there is a similar multiplicative relationship between the Ehrhart series for \(P\), for \(Q\), and for the free sum \(P\oplus Q\) that holds when \(P\) is reflexive and \(Q\) contains \(0\) in its interior.
We show that there is a similar multiplicative relationship between the Ehrhart series for \(P\), for \(Q\), and for the free sum \(P\oplus Q\) that holds when \(P\) is reflexive and \(Q\) contains \(0\) in its interior.
MSC:
| 52B20 | Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) |
| 52C07 | Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) |
