Fundamental polytopes of metric trees via parallel connections of matroids

We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.Comment: 20 pages, 2 Figures, 1 Table. Exposition improved, references and new results (last section) adde

Foundations for a theory of complex matroids

We explore a combinatorial theory of linear dependency in complex space, "complex matroids", with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of complex matroids, showing that this theory captures properties of linear dependency, orthogonality, and determinants over C in much the same way that oriented matroids capture the same properties over R. In addition, our complex matroids come with a canonical circle action analogous to the action of C* on a complex vector space. Our phirotopes (analogues of determinants) are the same as those studied previously by Below, Krummeck, and Richter-Gebert and by Delucchi. We further show that complex matroids cannot have vector axioms analogous to those for oriented matroids.Comment: 34 pages, exposition improved following a reviewer's suggestions, 2 figures adde

Inheritance of disc flower color in Helianthus petiolaris

Disc flowers of Helianthus petiolaris (Asteraceae) are usually purple reddue to anthocyanin pigments in corolla lobes, style and stigma. However, yellow-flowered plants are occasionally found. The inheritance of this trait wasstudied through crosses between different phenotypes and the results indicatedthat flower color is controlled by two genes with complementary action,both loci being dominant and independently inherited. This agrees with resultsobtained in cultivated sunflower, H. annuus, where one to three dominantgenes have been proposed for anthocyanin expression in different organs.Fil: Gutierrez, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; ArgentinaFil: Delucchi, C.. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Buenos Aires Norte. Estación Experimental Agropecuaria Pergamino; ArgentinaFil: Poverene, María Mónica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Centro de Recursos Naturales Renovables de la Zona Semiárida. Universidad Nacional del Sur. Centro de Recursos Naturales Renovables de la Zona Semiárida; Argentin