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Diagonalization and rationalization of algebraic Laurent series

Boris Adamczewski, Jason P. Bell (2013)

Annales scientifiques de l'École Normale Supérieure

We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime p the reduction modulo p of the diagonal of a multivariate algebraic power series f with integer coefficients is an algebraic power series of degree at most p A and height at most A p A , where A is an effective constant that only depends on...

Diameter-invariant graphs

Ondrej Vacek (2005)

Mathematica Bohemica

The diameter of a graph G is the maximal distance between two vertices of  G . A graph G is said to be diameter-edge-invariant, if d ( G - e ) = d ( G ) for all its edges, diameter-vertex-invariant, if d ( G - v ) = d ( G ) for all its vertices and diameter-adding-invariant if d ( G + e ) = d ( e ) for all edges of the complement of the edge set of G . This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.

Diamond representations of 𝔰𝔩 ( n )

Didier Arnal, Nadia Bel Baraka, Norman J. Wildberger (2006)

Annales mathématiques Blaise Pascal

In [6], there is a graphic description of any irreducible, finite dimensional 𝔰𝔩 ( 3 ) module. This construction, called diamond representation is very simple and can be easily extended to the space of irreducible finite dimensional 𝒰 q ( 𝔰𝔩 ( 3 ) ) -modules.In the present work, we generalize this construction to 𝔰𝔩 ( n ) . We show it is in fact a description of the reduced shape algebra, a quotient of the shape algebra of 𝔰𝔩 ( n ) . The basis used in [6] is thus naturally parametrized with the so called quasi standard Young tableaux....

Dichromatic number, circulant tournaments and Zykov sums of digraphs

Víctor Neumann-Lara (2000)

Discussiones Mathematicae Graph Theory

The dichromatic number dc(D) of a digraph D is the smallest number of colours needed to colour the vertices of D so that no monochromatic directed cycle is created. In this paper the problem of computing the dichromatic number of a Zykov-sum of digraphs over a digraph D is reduced to that of computing a multicovering number of an hypergraph H₁(D) associated to D in a natural way. This result allows us to construct an infinite family of pairwise non isomorphic vertex-critical k-dichromatic circulant...

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