11,684 research outputs found
Connected covering numbers
A connected covering is a design system in which the corresponding {\em block
graph} is connected. The minimum size of such coverings are called {\em
connected coverings numbers}. In this paper, we present various formulas and
bounds for several parameter settings for these numbers. We also investigate
results in connection with {\em Tur\'an systems}. Finally, a new general upper
bound, improving an earlier result, is given. The latter is used to improve
upper bounds on a question concerning oriented matroid due to Las Vergnas.Comment: 15 pages, 4 figures, 1 tabl
Matroid toric ideals: complete intersection, minors and minimal systems of generators
In this paper, we investigate three problems concerning the toric ideal
associated to a matroid. Firstly, we list all matroids such that
its corresponding toric ideal is a complete intersection.
Secondly, we handle with the problem of detecting minors of a matroid from a minimal set of binomial generators of . In
particular, given a minimal set of binomial generators of we
provide a necessary condition for to have a minor isomorphic to
for . This condition is proved to be sufficient
for (leading to a criterion for determining whether is
binary) and for . Finally, we characterize all matroids
such that has a unique minimal set of binomial generators.Comment: 9 page
Exponential type of hypercyclic entire functions
In this paper the exponential type of hypercyclic entire functions with respect to a
sequence (Φn(D)) of differential operators is considered, where every Φn is an entire
function of exponential type. We prove that under suitable conditions certain rates of
growth are possible for hypercyclicity while others are not. In particular, our statements extend the negative part of a sharp result on growth of D-hypercyclic entire functions due to Grosse-Erdmann, and are related to a result by Chan and Shapiro about the existence of Φ(D)-hypercyclic functions in certain Hilbert spaces of entire functions.Dirección General de Enseñanza Superior (DGES). EspañaJunta de Andalucí
Families of strongly annular functions: linear structure
A function f holomorphic in the unit disk D is called strongly annular if there exists a sequence of concentric circles in D expanding out to the unit circle such that f goes to infinity as |z| goes to 1 through these circles. The residuality of the family of strongly annular functions in the space of holomorphic functions on D is well known, and it is extended here to certain classes of functions. This important topological property is enriched in this paper by studying algebraic-topological properties of the mentioned family, in the modern setting of lineability. Namely, we prove that although this family is clearly nonlinear, it contains, except for the zero function, large vector subspaces as well as infinitely generated algebras. Similar results are obtained for strongly annular functions on the whole complex plane and for weighted Bergman spaces.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e Innovación (MICIN). EspañaMinisterio de Ciencia y Tecnología (MCYT). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER
Universality of holomorphic functions bounded on closed sets
In this note, the existence of translation-universal entire functions which are bounded on certain closed subsets is characterized in terms of topological and geometrical properties of such subsets. Corresponding results are also stated in the space of holomorphic functions on the unit disk and in the space of
harmonic functions on the plane. Moreover, it is shown the existence of entire functions which are bounded on many rays and, simultaneously, are universal with respect to a prescribed infinite-order differential operator.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superior (DGES). EspañaMinisterio de Ciencia y Tecnología (MCYT). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER
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