Alexander Engström: Ehrhart polynomials from ranking genes fast and a local Riemann hypothesis

In the methodology developed by Zohar Yakhini (Agilent Laboratories / the Technion) to compute what genes that are responsible for different diseases, statistical analysis of ranked lists is crucial. Together with Meromit Singer (UC Berkeley) I have tried to find fast ways to approximate certain partition functions that is a computational bottleneck. In this study we found pages of integers $\{a_{ij}\}_{i,j\geq 0}$ with the curious property that the functions $f_i(j)=a_{ij}$ and $g_i(j)=a_{ji}$ are Ehrhart polynomials for all $i$. Our first example of this was a page of binomial coefficients, and the next example was studied before by Pär Kurlberg et al. in the context of a local Riemann hypothesis. I will explain how to get more $\{a_{ij}\}_{i,j\geq 0}$ pages and discuss other connections.