Generalized Ehrhart polynomials

Let $P$ be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations $P(n) = nP$ is a quasi-polynomial in $n$. We generalize this theorem by allowing the vertices of P(n) to be arbitrary rational functions in $n$. In this case we prove that the number of lattice points in P(n) is a quasi-polynomial for $n$ sufficiently large. Our work was motivated by a conjecture of Ehrhart on the number of solutions to parametrized linear Diophantine equations whose coefficients are polynomials in $n$, and we explain how these two problems are related.Comment: 18 pages, no figures; v2: Sections 4 and 5 added, proofs and exposition have been expanded and clarifie

Ehrhart polynomials and stringy Betti numbers

We study the connection between stringy Betti numbers of Gorenstein toric varieties and the generating functions of the Ehrhart polynomials of certain polyhedral regions. We use this point of view to give counterexamples to Hibi's conjecture on the unimodality of delta-vectors of reflexive polytopes.Comment: 8 pages; revised version: added reference to paper of Batyrev-Dais, combinatorial proof of Theorem 1.3 included; to appear in Math. An

Impact of Conditional Cash Transfers and Remittances on Credit Market Outcomes in Rural Nicaragua

The impact of public and private transfers on credit markets has not been sufficiently studied and understanding any spill over effects caused by these transfers may be useful for policy makers. This paper estimates the impact of Conditional Cash Transfers (CCTs) and remittances received by poor households in rural Nicaragua on their decision to request a loan. We find that, on average, CCTs did not affect the request of credit while remittances increased it, controlling for potential endogeneity. We argue the reduction in income risk provided by remittances changes borrowers’ expected marginal returns to a loan and/or their creditworthiness, as perceived by lenders. The successful enforcement of the use of CCTs on long-term investments seems to have avoided externalities on the use of short-term credit these households have access to and their creditworthiness.International Development, D14, F22, O15,