Parity of transversals of Latin squares

We introduce a notion of parity for transversals, and use it to show that in Latin squares of order $2 \bmod 4$, the number of transversals is a multiple of 4. We also demonstrate a number of relationships (mostly congruences modulo 4) involving $E_1,\dots, E_n$, where $E_i$ is the number of diagonals of a given Latin square that contain exactly $i$ different symbols. Let $A(i\mid j)$ denote the matrix obtained by deleting row $i$ and column $j$ from a parent matrix $A$. Define $t_{ij}$ to be the number of transversals in $L(i\mid j)$, for some fixed Latin square $L$. We show that $t_{ab}\equiv t_{cd}\bmod2$ for all $a,b,c,d$ and $L$. Also, if $L$ has odd order then the number of transversals of $L$ equals $t_{ab}$ mod 2. We conjecture that $t_{ac} + t_{bc} + t_{ad} + t_{bd} \equiv 0 \bmod 4$ for all $a,b,c,d$. In the course of our investigations we prove several results that could be of interest in other contexts. For example, we show that the number of perfect matchings in a $k$-regular bipartite graph on $2n$ vertices is divisible by $4$ when $n$ is odd and $k\equiv0\bmod 4$. We also show that $${\rm per}\, A(a \mid c)+{\rm per}\, A(b \mid c)+{\rm per}\, A(a \mid d)+{\rm per}\, A(b \mid d) \equiv 0 \bmod 4$$ for all $a,b,c,d$, when $A$ is an integer matrix of odd order with all row and columns sums equal to $k\equiv2\bmod4$

Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group

We show the Alon-Tarsi conjecture on Latin squares is equivalent to a very special case of a conjecture made independently by Hadamard and Howe, and to the non-vanishing of some interesting integrals over SU(n). Our investigations were motivated by geometric complexity theory.Comment: 7 page

Intersection between class and gender and its effect on the quality of employment in Chile

Indexación: Web of Science; Scopus.En este artículo se analiza el efecto de la intersección entre clase y género sobre la calidad del empleo en Chile. La medida de posición de clase utilizada está basada en la propuesta de Erik O. Wright y la calidad del empleo en una medida multidimensional, que incluye un índice de condiciones objetivas de empleo y dos índices de condiciones subjetivas (motivación en el trabajo y percepción del control sobre el proceso de trabajo). Los resultados demuestran que la clase y el género determinan diferencias significativas en la calidad objetiva y subjetiva del empleo. Sin embargo, los datos también indican que el género (particularmente, el hecho de ser mujer) no actúa necesariamente como “amplificador” de las desigualdades de clase observadas en el mercado laboral. A partir de esto, al final del artículo se plantean algunas reflexiones sobre cómo opera la intersección entre clase y género en el mercado laboral chileno.This study explores the impact of the intersection between class and gender on the quality of employment in Chile. The method used to measure social class position is based on the work of Erik O. Wright, while, for the quality of employment, a multidimensional measurement was used, including one index for objective working conditions and two indices for subjective ones (motivation on the job and the perception of control over work processes). The results demonstrate that class and gender give rise to signifcant differences in objective and subjective job quality. However, the data also indicate that gender (more specifcally, the fact of being female) does not necessarily amplify the class-based inequalities observed in the labour market. Drawing on these fndings, a number of thoughts about how the class/gender intersection operates in the Chilean labour market are shared in the fnal section of this studyhttp://hdl.handle.net/11362/4079

Crime and Social media

Purpose-The study complements the scant macroeconomic literature on the development outcomes of social media by examining the relationship between Facebook penetration and violent crime levels in a cross-section of 148 countries for the year 2012. Design/methodology/approach-The empirical evidence is based on Ordinary Least Squares (OLS), Tobit and Quantile regressions. In order to respond to policy concerns on the limited evidence on the consequences of social media in developing countries, the dataset is disaggregated into regions and income levels. The decomposition by income levels included: low income, lower middle income, upper middle income and high income. The corresponding regions include: Europe and Central Asia, East Asia and the Pacific, Middle East and North Africa, Sub-Saharan Africa and Latin America. Findings-From OLS and Tobit regressions, there is a negative relationship between Facebook penetration and crime. However, Quantile regressions reveal that the established negative relationship is noticeable exclusively in the 90th crime decile. Further, when the dataset is decomposed into regions and income levels, the negative relationship is evident in the Middle East and North Africa (MENA) while a positive relationship is confirmed for sub-Saharan Africa. Policy implications are discussed. Originality/value- Studies on the development outcomes of social media are sparse because of a lack of reliable macroeconomic data on social media. This study primarily complemented three existing studies that have leveraged on a newly available dataset on Facebook

Proceedings of the Conference on Emerging Economic Issues in a Globalizing World

This paper tests the endogenous relationship between FDI and economic growth using a panel dataset for 23 OECD countries for the period 1975-2004. Following the literature, we treat economic growth and FDI as endogenous variables, and estimate a two-equation simultaneous equation system with the generalized methods of moments (GMM) for the OECD case. We find that FDI and growth are important determinants of for each other. We also find that export growth rate is statistically significant determinant of FDI and economic growth. Our results indicate that there is an endogenous relationship between FDI and economic growth.FDI, growth

Social Mobility in Latin America: A Review of Existing Evidence

This paper reviews evidence on social mobility in Latin America. Several studies have used data sets that collect intergenerational socio economic information. The data, though limited, suggest that social mobility is low in the region, even when compared with low social mobility developed countries like the United States and United Kingdom, with high levels of immobility at the lower and upper tails of the income distribution. While Latin America has improved education mobility in recent decades, which may have translated into higher mobility for younger cohorts, the region still presents, except for Chile, lower education mobility than in developed countries. The paper also reviews studies on the main determinants of the region’s low levels of social mobility, including social exclusion, low access to higher education, and labor market discrimination.Social mobility, Latin America, Inequality, Social Exclusion, Education

Explaining export regional involvement through marketing strategy : the case of Spanish companies exporting to Latin America

The equivalence between the absence of arbitrage and the existence of an equivalent martingale measure fails when an infinite number of trading dates is considered. By enlarging the set of states of nature and the probability measure through a projective system of topological spaces and Radon measures, we characterize the absence of arbitrage when the time set is countable