769 research outputs found

    Permutation Patterns, Reduced Decompositions with Few Repetitions and the Bruhat Order

    Get PDF
    This thesis is concerned with problems involving permutations. The main focus is on connections between permutation patterns and reduced decompositions with few repetitions. Connections between permutation patterns and reduced decompositions were first studied various mathematicians including Stanley, Billey and Tenner. In particular, they studied pattern avoidance conditions on reduced decompositions with no repeated elements. This thesis classifies the pattern avoidance and containment conditions on reduced decompositions with one and two elements repeated. This classification is then used to obtain new enumeration results for pattern classes related to the reduced decompositions and introduces the technique of counting pattern classes via reduced decompositions. In particular, counts on pattern classes involving 1 or 2 copies of the patterns 321 and 3412 are obtained. Pattern conditions are then used to classify and enumerate downsets in the Bruhat order for the symmetric group and the rook monoid which is a generalization of the symmetric group. Finally, motivated by coding theory, the concepts of displacement, additive stretch and multiplicative stretch of permutations are introduced. These concepts are then analyzed with respect to maximality and distribution as a new prospect for improving interleaver design

    Exploring the space between: Social networks, trust, and urban school district leaders

    Full text link
    Una serie de académicos han estudiado el contexto del distrito en el que se encuentran inmersos los centros educativos. Estos estudios sugieren la importancia de las oficinas municipales como apoyo o limitación del trabajo de los centros educativos ofreciendo estrategias para construir las relaciones entre los distritos y los líderes locales. Esta es una tarea importante y, sin embargo, frecuentemente se pasa por alto que las mejoras de los esfuerzos organizativos se construyen socialmente. Por ello, el análisis de las redes sociales y la confianza entre los líderes del distrito y de los centros educativos puede proporcionar una visión desde dentro respecto a los apoyos y limitaciones relacionados con la mejora. En este estudio de caso se utiliza una red social y datos sobre la confianza para explorar las mejores prácticas relacionadas con los líderes, en un distrito escolar de tamaño medio con bajo rendimiento. Los resultados sugieren unos lazos sociales de la red débiles, bajos niveles de confianza y una previsible relación entre la confianza y los intercambios recíprocos con las mejores prácticas relacionadas con la mejoraA number of scholars are exploring the district context in which schools are embedded. These studies suggest the importance of the district office as a support or constraint to the work of schools and offer strategies for building relations between district and site leaders. While this is an important task, what is frequently overlooked is that organizational improvement efforts are often socially constructed. Therefore, an analysis of social networks and trust between district and site leaders may provide additional insights into supports and constraints related to improvement. This case study uses social network and trust data to explore the underlying best practice relations between leaders in a midsize underperforming urban school district. Results suggest weak network ties, low levels of trust, and a predictive relationship between trust and the reciprocal exchange of best practices related to improvementEsta investigación ha sido apoyada por una financiación de la W.T. Grant Foundation (Grant, nº 10174

    #commoncore Project: How Social Media Is Changing the Politics of Education

    Get PDF
    The Common Core has become a flashpoint at the nexus of education politics and policy, fueled by ardent social media activists. To explore this phenomenon, this innovative and interactive website examines the Common Core debate through the lens of the influential social media site Twitter. Using a social network perspective that examines the relationships among actors, we focus on the most highly used Twitter hashtag about the Common Core: #commoncore. The central question of our investigation is: How are social media-enabled social networks changing the discourse in American politics that produces and sustains social policy? To join a conversation about this research in an open forum, tweet using #htagcommoncore

    #CommonCore: Methods

    Get PDF
    This section provides a detailed discussion of the methods used to arrive at the conclusions in #CommonCore: How social media is changing the politics of education

    Community Foundations: Egypt

    Get PDF
    This paper deals with community foundations in Egyp
    • …
    corecore