Kronecker products and the RSK correspondence

The starting point for this work is an identity that relates the number of minimal matrices with prescribed 1-marginals and coefficient sequence to a linear combination of Kronecker coefficients. In this paper we provide a bijection that realizes combinatorially this identity. As a consequence we obtain an algorithm that to each minimal matrix associates a minimal component, with respect to the dominance order, in a Kronecker product, and a combinatorial description of the corresponding Kronecker coefficient in terms of minimal matrices and tableau insertion. Our bijection follows from a generalization of the dual RSK correspondence to 3-dimensional binary matrices, which we state and prove. With the same tools we also obtain a generalization of the RSK correspondence to 3-dimensional integer matrices

Stability of Kronecker coefficients via discrete tomography

In this paper we give a new sufficient condition for a general stability of Kronecker coefficients, which we call it additive stability. It was motivated by a recent talk of J. Stembridge at the conference in honor of Richard P. Stanley's 70th birthday, and it is based on work of the author on discrete tomography along the years. The main contribution of this paper is the discovery of the connection between additivity of integer matrices and stability of Kronecker coefficients. Additivity, in our context, is a concept from discrete tomography. Its advantage is that it is very easy to produce lots of examples of additive matrices and therefore of new instances of stability properties. We also show that Stembridge's hypothesis and additivity are closely related, and prove that all stability properties of Kronecker coefficients discovered before fit into additive stability.Comment: 22 page

Alcohol Use In Mexican-Americans By Nativity: The Role Of Ethnic Identity, Acculturation, And Acculturative Stress

The present study examined alcohol use disorder symptoms among Mexican-Americans. Participants consisted of a community-based sample of 237 Mexican-American adults living in the Midwest United States. The role of nativity status and cultural variables in alcohol use disorder symptoms was explored. Specifically, ethnic identity, acculturation, and acculturative stress were used to predict membership into high and low alcohol use disorder symptom groups among U.S.-and foreign-born Mexican-Americans. Additionally, gender, ethnic identity, and acculturative stress were tested as moderators in the relationship between acculturation and alcohol use disorder symptoms. Among U.S.-born participants, only ethnic identity was found to be predictive of alcohol use disorder symptoms, such that higher ethnic identity was related to fewer alcohol use disorder symptoms. Among foreign-born participants, ethnic identity was also predictive of few alcohol use disorder symptoms. Additionally, increased pressure against acculturation was predictive of higher alcohol use disorder symptoms for foreign-born participants. Among the sample as a whole, those with low Latino Orientation and high pressure against acculturation reported more alcohol use disorder symptoms. These results highlight the protective effect of ethnic identity and the need for further research that examines nativity status, acculturation, and specific acculturative stressors in regard to alcohol use disorder symptoms among Mexican-Americans

Preventing a Risk/Risk Trade-off: An Analysis of the Measures Necessary to Increase U.S. Pollinator Numbers

This Note will proceed in four parts. Part II will discuss the importance of pollinators and the possible reasons for their declining numbers. Part III will delve into the current and proposed actions to increase pollinator populations that are taking place in the United States. Part IV will then discuss the generally desired and widely accepted solution: a ban on neonicotinoids. This Part will introduce the implementation and results of a neonicotinoid ban in the European Union, and the risk/risk trade-off presented by a neonicotinoid ban. Finally, Part V will compile the solutions discussed in Parts III and IV, and present possible legal and administrative solutions that can be put in place to protect bees, modeled after the legal actions that have successfully increased monarch butterfly populations while avoiding the issues the European Union faced with its neonicotinoid ban. Part V will conclude that banning neonicotinoids is not the save-all solution to pollinator decline, and propose that focusing on a multiplicity of avenues—both legal and administrative—that tackle the many reasons why pollinator populations are in decline is more likely to increase pollinator numbers than focusing on one single facto

A generalized index of market power

This paper analyses two approaches to measuring market power-the commonly used Lerner index and a range of exploitation measures-. Itis argued that the Lerner index is designed to quantify market power fromthe supply side and the exploitation measures are designed to quantify marketpower from the demand side, and that the two approaches do not always behavein a symmetric way, since they do not always have the same bounds. To sortout these potentially undesirable properties, this paper proposes a new generalindex to measure market power, which is symmetrical in the sense that it isbounded between zero and one, regardless of whether the market power comesfrom the supply or the demand side. The index proposed allows for the presenceof more than one firm and for the existence of conjectural variations.*******************************************************************************************************************Este documento analiza dos enfoques para medir poder de mercado-el frecuentemente utilizado índice de Lerner y un conjunto de medidas de explotación-. Se argumenta que el índice de Lerner está diseñado para cuantificarel poder de mercado por el lado de la oferta y que las medidas de explotaciónestán diseñadas para cuantificar el poder de mercado por el lado de la demanda,y que esos dos enfoques no siempre tienen los mismos límites. Paracorregir estas propiedades potencialmente no deseables, este documento proponeun nuevo índice general para medir poder de mercado, que es simétrico-estando restringido a valores entre cero y uno-, independientemente de si elpoder de mercado proviene del lado de la oferta o de la demanda. El índice propuestopermite la presencia de más de una firma y la existencia de variacionesconjeturales.market power, mark up, mark down, Lerner index, exploitation measures, industrial organization, conjectural variations