The topology of the external activity complex of a matroid

We prove that the external activity complex $\textrm{Act}_<(M)$ of a matroid is shellable. In fact, we show that every linear extension of LasVergnas's external/internal order $<_{ext/int}$ on $M$ provides a shelling of $\textrm{Act}_<(M)$. We also show that every linear extension of LasVergnas's internal order $<_{int}$ on $M$ provides a shelling of the independence complex $IN(M)$. As a corollary, $\textrm{Act}_<(M)$ and $M$ have the same $h$-vector. We prove that, after removing its cone points, the external activity complex is contractible if $M$ contains $U_{3,1}$ as a minor, and a sphere otherwise.Comment: Comments are welcom

Coxeter submodular functions and deformations of Coxeter permutahedra

We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This family of polytopes contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra, polymatroids, and submodular functions to any finite reflection group.Comment: Minor edits. To appear in Advances of Mathematic

Finiteness theorems for matroid complexes with prescribed topology

It is known that there are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating to the language of $h$-vectors, there are finitely many simplicial complexes of bounded dimension with $h_1=k$ for any natural number $k$. In this paper we study the question at the other end of the $h$-vector: Are there only finitely many $(d-1)$-dimensional simplicial complexes with $h_d=k$ for any given $k$? The answer is no if we consider general complexes, but when focus on three cases coming from matroids: (i) independence complexes, (ii) broken circuit complexes, and (iii) order complexes of geometric lattices. We prove the answer is yes in cases (i) and (iii) and conjecture it is also true in case (ii).Comment: to appear in European Journal of Combinatoric

The Basic Statute for Public Employees: the Powers of the Autonomous Governments

El treball  que es presenta és un estudi de les competències autonòmiques en matèria d'ocupació  pública i, molt especialment, d'allò que es refereix a les competències assumides per Catalunya en virtut de les reformes estatutàries esdevingudes en els últims anys i la incidència de la jurisprudència constitucional sobre aquestes reformes esdevinguda com a conseqüència de l'examen de la constitucionalitat del nou Estatut d'autonomia.El trabajo que se presenta es un estudio de las competencias autonómicas en materia de empleo público y, muy especialmente, en aquello que se refiere a las competencias asumidas por Cataluña en virtud de las reformas estatutarias acontecidas en los últimos años y la incidencia en las mismas de la jurisprudencia constitucional emitida como consecuencia del examen de la constitucionalidad del nuevo Estatuto de autonomía.This paper studies the powers of the governments of the autonomous regions with respect to public employment, in particular, 1) the powers taken on by Catalonia as a result of the statutory reforms of recent years, and 2) the impact on these powers of the constitutional case law that has developed as a result of the challenges to the constitutionality of the new Statute of Autonomy.

Roadblocks to the Implementation of Problem-Oriented Policing in Montevideo

In the broad context of Uruguay’s police reform, the Ministry of Interior is implementing a pilot Problem-Oriented Policing (POP) program in Montevideo since late 2012. This research examined the obstacles confronted by the program throughout its implementation. Using a grounded theory approach, qualitative data was collected through 20 semi-structured interviews with members of the Uruguay National Police (UNP) of different ranks. Findings were analyzed based on the following categories: a) contextual factors; b) theoretical and practical inaccuracies; c) characteristics, skills and actions of project managers; d) resistance and motivational issues; e) resources; f) external support and cooperation. Consistent with research conducted on POP in other settings, findings suggest the program confronted a diverse set of obstacles over its implementation corresponding to all but one of the proposed categories. The study concludes with a series of recommendations to inform future POP endeavors by the UNP

The topology of the external activity complex of a matroid

International audienceWe prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of Las Vergnas's external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of Las Vergnas's internal order <int on M provides a shelling of the independence complex IN(M). As a corollary, Act<(M) and M have the same h-vector. We prove that, after removing its cone points, the external activity complex is contractible if M contains U3,1 as a minor, and a sphere otherwise

Los derechos enfrentados de los consumidores, productores y comercializadores de leche en Colombia

142 P?ginasRecurso Electr?nicoINTRODUCCI?N 12 1. FORMULACI?N DEL PROBLEMA 13 1.1. DESCRIPCI?N DEL PROBLEMA 13 1.2. FORMULACI?N DEL PROBLEMA 15 1.2.1. Problema general 15 1.2.2. Problemas espec?ficos 15 2. JUSTIFICACI?N 16 3. OBJETIVOS 22 3.1. OBJETIVO GENERAL 22 3.2. OBJETIVOS ESPEC?FICOS 22 4. METODOLOG?A 23 4.1. TIPO DE ESTUDIO 23 4.2. FASES DE LA INVESTIGACI?N 24 4.2.1. El dise?o emergente 25 4.2.2. Recolecci?n de la informaci?n 25 4.2.2.1. Fuentes Secundarias 26 4.2.2.2. Fuentes Primarias 26 4.2.3. Organizaci?n y an?lisis de la informaci?n 27 4.2.4. Elaboraci?n del caso did?ctico 27 5. MARCO REFERENCIAL 28 5.1. ANTECEDENTES 28 5.2. MARCO TE?RICO 35 5.2.1. Leche 35 4 5.2.1.1. Caracter?sticas de la Leche 35 5.2.1.2. Composici?n de la Leche 36 5.2.1.3. Importancia de la leche 37 5.2.1.4. Microorganismos presentes en la leche 37 5.2.2. Factores que influyen en la calidad de la leche 38 5.2.2.1. Nutrici?n 38 5.2.2.2. Contaminaci?n dentro de la gl?ndula mamaria 38 5.2.2.3. Cuidados del gl?ndula mamaria 38 5.2.3. La inocuidad en la producci?n de leche 39 5.2.4. Comercializaci?n de leche cruda 40 5.2.5. La industria l?ctea en Colombia 40 5.2.6. La comercializaci?n de leche en Colombia 42 5.2.7. Tensi?n entre derechos humanos 43 5.2.8. La salud como derecho 46 5.3. MARCO LEGAL 48 6. RESULTADOS DE LA INVESTIGACI?N 54 6.1. ENCUESTA A PRODUCTORES DE LECHE 54 6.2. ENCUESTA APLICADA A CONSUMIDORES AFECTADOS 72 6.3. ENCUESTA APLICADA A AUTORIDAD SANITARIA 82 7. CASO DID?CTICO 93 7.1. NARRATIVA 93 7.2. GU?A DEL DOCENTE 110 7.2.1. Gu?a pedag?gica para la aplicaci?n del caso did?ctico 110 8. CONCLUSIONES 118 RECOMENDACIONES 121 REFERENCIAS 12

On the Todd Class of the Permutohedral variety

In the special case of braid fans, we give a combinatorial formula for the Berline-Vergne's construction for an Euler-Maclaurin type formula that computes number of lattice points in polytopes. Our formula is obtained by computing a symmetric expression for the Todd class of the permutohedral variety. By showing that this formula does not always have positive values, we prove that the Todd class of the permutohedral variety $X_d$ is not effective for $d\geq 24$. Additionally, we prove that the linear coefficient in the Ehrhart polynomial of any lattice generalized permutohedron is positive.Comment: 22 pages, 7 figure

Ehrhart Positivity for Generalized Permutohedra

International audienceThere are few general results about the coefficients of Ehrhart polynomials. We present a conjecture about their positivity for a certain family of polytopes known as generalized permutohedra. We have verified the conjecture for small dimensions combining perturbation methods with a new valuation on the algebra of rational pointed polyhedral cones constructed by Berline and Vergne.Il existe peu de résultats sur les coefficients des polynômes d’Ehrhart. On présente une conjecture concernant leur positivité pour une certaine famille de polytopes connus sous le nom de permutoèdre généralisé. On a vérifié la conjecture pour les petites dimensions en combinant des méthodes de perturbation avec une nouvelle valuation sur l’algèbre des cônes polyédraux rationnels pointés, construite par Berline et Vergne