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Enveloppe convexe des hyperplans d’un espace affine fini

Olivier Anglada, Jean François Maurras (2003)

RAIRO - Operations Research - Recherche Opérationnelle

Dans cet article nous caractérisons, par les facettes, l’enveloppe convexe des vecteurs caractéristiques des hyperplans d’un espace projectif fini et d’un espace affine fini.

Enveloppe convexe des hyperplans d'un espace affine fini

Olivier Anglada, Jean François Maurras (2010)

RAIRO - Operations Research

Dans cet article nous caractérisons, par les facettes, l'enveloppe convexe des vecteurs caractéristiques des hyperplans d'un espace projectif fini et d'un espace affine fini.

Equations relating factors in decompositions into factors of some family of plane triangulations, and applications (with an appendix by Andrzej Schinzel)

Jan Florek (2015)

Colloquium Mathematicae

Let be the family of all 2-connected plane triangulations with vertices of degree three or six. Grünbaum and Motzkin proved (in dual terms) that every graph P ∈ has a decomposition into factors P₀, P₁, P₂ (indexed by elements of the cyclic group Q = 0,1,2) such that every factor P q consists of two induced paths of the same length M(q), and K(q) - 1 induced cycles of the same length 2M(q). For q ∈ Q, we define an integer S⁺(q) such that the vector (K(q),M(q),S⁺(q)) determines the graph P (if P is...

Equidecomposability of Jordan domains under groups of isometries

M. Laczkovich (2003)

Fundamenta Mathematicae

Let G d denote the isometry group of d . We prove that if G is a paradoxical subgroup of G d then there exist G-equidecomposable Jordan domains with piecewise smooth boundaries and having different volumes. On the other hand, we construct a system d of Jordan domains with differentiable boundaries and of the same volume such that d has the cardinality of the continuum, and for every amenable subgroup G of G d , the elements of d are not G-equidecomposable; moreover, their interiors are not G-equidecomposable...

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