Subword complexes via triangulations of root polytopes

Subword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any subword complex is homeomorphic to a ball or a sphere and asked about their geometric realizations. We show that a family of subword complexes can be realized geometrically via regular triangulations of root polytopes. This implies that a family of $\beta$-Grothendieck polynomials are special cases of reduced forms in the subdivision algebra of root polytopes. We can also write the volume and Ehrhart series of root polytopes in terms of $\beta$-Grothendieck polynomials.Comment: 17 pages, 15 figure

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

The multidegree of the multi-image variety

The multi-image variety is a subvariety of Gr(1,P^3)^n that models taking pictures with n rational cameras. We compute its cohomology class in the cohomology of Gr(1,P^3)^n, and from there its multidegree as a subvariety of (P^5)^n under the Pl\"ucker embedding.Comment: 16 pages, 5 figures, 1 tabl

K-orbit closures and Barbasch-Evens-Magyar varieties

We define the Barbasch-Evens-Magyar variety. We show it is isomorphic to the smooth variety defined in [D. Barbasch-S. Evens '94] that maps finite-to-one to a symmetric orbit closure, thereby giving a resolution of singularities in certain cases. Our definition parallels [P. Magyar '98]'s construction of the Bott-Samelson variety [H. C. Hansen '73, M. Demazure '74]. From this alternative viewpoint, one deduces a graphical description in type A, stratification into closed subvarieties of the same kind, and determination of the torus-fixed points. Moreover, we explain how these manifolds inherit a natural symplectic structure with Hamiltonian torus action. We then prove that the moment polytope is expressed in terms of the moment polytope of a Bott-Samelson variety.Comment: 26 pages, 4 figure

Progressive care : an examination of male to female transgender sex workers\u27 experiences within the health care and social service systems in San Francisco, California

This qualitative study explores male to female transgender sex workers\u27 experiences within the social service and health care systems in San Francisco, California. Twenty one male to female transgender sex worker participants were asked to rate services provided to them by the social service and health care systems. Ten of these participants were then asked a series of questions about their experiences within the social service and health care systems in San Francisco. Participants\u27 racial identities and ages were not diverse. Most participants identified as African American and their ages fell between the ranges of 41 and 50 within this study. All participants had worked as sex workers and accessed social services and health care within the last five years. Participants rated health care and social services positively and discussed areas in which these systems could better address for the male to female transgender sex worker community in San Francisco. The major findings reveal the positive services that male to female transgender sex workers have experienced from health care and social services in San Francisco. These findings also reveal the continued discrimination this group faces within these systems and the work force, and the continued violence and health risks they face on the streets. Lastly, this study implicates the need for job trainings for this group and sensitivity trainings for providers and the general public

Aternativas a la supresión del impuesto sobre el patrimonio

La Imposición Personal sobre la Riqueza atraviesa en España un momento crítico, incluso el Impuesto sobre el Patrimonio Neto ha sido suprimido para el ejercicio 2008, argumentando en su contra su excesiva complejidad y efectos desincentivo a la entrada de inversiónes. Realmente desde que este Impuesto se cedió a las Comunidades Autónomas, únicamente ha interesado su potencial recaudador que, al no ser muy alto, le ha situado en una posición muy secundaria como instrumento de financiación autonómica. Sin embargo, el debate académico, desde un enfoque más teórico-analítico, ha estado totalmente ausente en su supresión. En este trabajo se intenta estimular el interés sobre el papel que este impuesto puede desarrollar como parte integrante de un sistema tributario moderno. En este sentido se recuerdan los argumentos teóricos que tradicionalmente se han esbozado a favor y en contra de este tipo de imposición; se ofrece un análisis económico de la incidencia y efectos redistributivos del Impuesto sobre el Patrimonio Neto estudiando, además, su labor como complemento del Impuesto sobre la Renta de las Personas físicas. Finalmente se reflexiona acerca de diferentes alternativas futuras de reforma del Impuesto, valorando las posibles ventajas de éstas frente a su supresión