On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

The impact of foreign ownership and off-shore investing on technical efficiency: evidence from Chinese managed funds industry

In a landmark reform in the managed fund industry, China permitted foreign joint ventures as well as off-shore investing. Have these decisions helped improved the efficiency of the industry? We examine this hitherto unexamined question in the literature, using a robust method of efficiency analysis—bootstrap data envelopment analysis. We compute the bootstrap efficiency scores and regress them using truncated regression on environmental variables. We focus on 64 of 69 funds management companies in China from 2003 to 2011 using a unique dataset made available to us. We find that there is considerable room for funds management companies to improve technical efficiency to ultimately bring increased benefits to investors. We find that foreign ownership has not helped efficiency improvement. Similarly, off-shore investing had no impact on technical efficiency. A number of regulatory constraints still persist in China, which makes it hard for the previously measured to yield efficiency gains. We recommend further liberalization of the sector, for example, by removing restriction on distribution of foreign funds