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A Pieri-type formula for even orthogonal Grassmannians

Piotr Pragacz, Jan Ratajski (2003)

Fundamenta Mathematicae

We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...

A polyhedral study of a two level facility location model

Mourad Baïou, Francisco Barahona (2014)

RAIRO - Operations Research - Recherche Opérationnelle

We study an uncapacitated facility location model where customers are served by facilities of level one, then each level one facility that is opened must be assigned to an opened facility of level two. We identify a polynomially solvable case, and study some valid inequalities and facets of the associated polytope.

A polynomial algorithm for minDSC on a subclass of series Parallel graphs

Salim Achouri, Timothée Bossart, Alix Munier-Kordon (2009)

RAIRO - Operations Research

The aim of this paper is to show a polynomial algorithm for the problem minimum directed sumcut for a class of series parallel digraphs. The method uses the recursive structure of parallel compositions in order to define a dominating set of orders. Then, the optimal order is easily reached by minimizing the directed sumcut. It is also shown that this approach cannot be applied in two more general classes of series parallel digraphs.

A Poster about the Old History of Fractional Calculus

Tenreiro Machado, J., Kiryakova, Virginia, Mainardi, Francesco (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.

A prime factor theorem for a generalized direct product

Wilfried Imrich, Peter F. Stadler (2006)

Discussiones Mathematicae Graph Theory

We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.

A problem of Rankin on sets without geometric progressions

Melvyn B. Nathanson, Kevin O'Bryant (2015)

Acta Arithmetica

A geometric progression of length k and integer ratio is a set of numbers of the form a , a r , . . . , a r k - 1 for some positive real number a and integer r ≥ 2. For each integer k ≥ 3, a greedy algorithm is used to construct a strictly decreasing sequence ( a i ) i = 1 ∞ of positive real numbers with a₁ = 1 such that the set G ( k ) = ⋃ i = 1 ∞ ( a 2 i , a 2 i - 1 ] contains no geometric progression of length k and integer ratio. Moreover, G ( k ) is a maximal subset of (0,1] that contains no geometric progression of length k and integer ratio. It is also proved that there is...

A proof of menger's theorem by contraction

Frank Göring (2002)

Discussiones Mathematicae Graph Theory

A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph.

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