Newton polytopes and symmetric Grothendieck polynomials

Symmetric Grothendieck polynomials are inhomogeneous versions of Schur polynomials that arise in combinatorial $K$-theory. A polynomial has saturated Newton polytope (SNP) if every lattice point in the polytope is an exponent vector. We show Newton polytopes of these Grothendieck polynomials and their homogeneous components have SNP. Moreover, the Newton polytope of each homogeneous component is a permutahedron. This addresses recent conjectures of C. Monical-N. Tokcan-A. Yong and of A. Fink-K. M\'esz\'aros-A. St. Dizier in this special case.Comment: 4 pages, 1 figur

Free subgroups of free products and combinatorial hypermaps

We derive a generating series for the number of free subgroups of finite index in $\Delta^+ = \mathbb{Z}_p*\mathbb{Z}_q$ by using a connection between free subgroups of $\Delta^+$ and certain hypermaps (also known as ribbon graphs or "fat" graphs), and show that this generating series is transcendental. We provide non-linear recurrence relations for the above numbers based on differential equations that are part of the Riccati hierarchy. We also study the generating series for conjugacy classes of free subgroups of finite index in $\Delta^+$, which correspond to isomorphism classes of hypermaps. Asymptotic formulas are provided for the numbers of free subgroups of given finite index, conjugacy classes of such subgroups, or, equivalently, various types of hypermaps and their isomorphism classes.Comment: 27 pages, 3 figures; supplementary SAGE worksheets available at http://sashakolpakov.wordpress.com/list-of-papers

Bodily injuries and dative experiencers in Old Frisian

This article offers a descriptive account of body part constructions in Old East Frisian texts and analyzes the occurrence of dative experiencers in such clauses. This includes a comparison between Old Frisian body part grammar and its Middle Dutch counterpart, revisiting issues such as the antiquity of dative external possessors and oblique subject constructions in West Germanic. In presenting the data from a theory-neutral perspective, this investigation contributes to the study of body part grammar in Medieval Germanic in particular and to the growing body of literature on Old Frisian syntax in general

Elliptic Selberg integrals and conformal blocks

We present an elliptic version of Selberg's integral formula.Comment: 13 page

Three-dimensional maps and subgroup growth

In this paper we derive a generating series for the number of cellular complexes known as pavings or three-dimensional maps, on $n$ darts, thus solving an analogue of Tutte's problem in dimension three. The generating series we derive also counts free subgroups of index $n$ in $\Delta^+ = \mathbb{Z}_2*\mathbb{Z}_2*\mathbb{Z}_2$ via a simple bijection between pavings and finite index subgroups which can be deduced from the action of $\Delta^+$ on the cosets of a given subgroup. We then show that this generating series is non-holonomic. Furthermore, we provide and study the generating series for isomorphism classes of pavings, which correspond to conjugacy classes of free subgroups of finite index in $\Delta^+$. Computational experiments performed with software designed by the authors provide some statistics about the topology and combinatorics of pavings on $n\leq 16$ darts.Comment: 17 pages, 6 figures, 1 table; computational experiments added; a new set of author

Have US-Funded CARSI Programs Reduced Crime and Violence in Central America? An Examination of LAPOP'S Impact Assessment of US Violence Prevention Programs in Central America

In October 2014, the Latin American Public Opinion Project (LAPOP) at Vanderbilt University published an impact assessment study of community-based violence prevention programs that have been implemented under the umbrella of the US State Department's Central American Regional Security Initiative (CARSI). The study looked at survey data measuring public perceptions of crime in 127 treatment and control neighborhoods in municipalities in El Salvador, Guatemala, Honduras, and Panama where the violence prevention programs have been implemented. The study's authors stated that the data shows that "in several key respects the programs have been a success" and note, for instance, that 51 percent fewer residents of "treated" communities reported being aware of murders and extortion incidents during the previous 12 months, and 19 percent fewer residents reported having heard about robberies having occurred.As the LAPOP study is, to date, the only publicly accessible impact assessment of programs carried out under CARSI -- a notoriously opaque regional assistance scheme that has received hundreds of millions of dollars of US government funding -- a thorough review of the LAPOP study data seemed appropriate.The following report examines the data collected during the LAPOP study and subjects them to a number of statistical tests. The authors find that the study cannot support the conclusion that the areas subject to treatment in the CARSI programs showed better results than those areas that were not.This report identifies major problems with the LAPOP study, namely, the nonrandomness of the selection of treatment versus control areas and how the differences in initial conditions, as well as differences in results between treatment and control areas, have been interpreted. In the case of reported robberies, if the areas subject to treatment have an elevated level of reported robberies in the year prior to treatment, it is possible that there is some reversion to normal levels over the next year. The LAPOP methodology does not differentiate between effective treatment and, for example, an unrelated decline in reported robberies in a treated area following a year with an abnormally high number of reported robberies. The series of statistical tests in this report indicate that this possibility is quite plausible, and cannot be ruled out; and that the LAPOP study, therefore, does not demonstrate a statistically significant positive effect of treatment. The same can be said for the other variables where the LAPOP study finds significant improvement