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The Tutte polynomial of a morphism of matroids I. Set-pointed matroids and matroid perspectives

Michel Las Vergnas (1999)

Annales de l'institut Fourier

We study the basic algebraic properties of a 3-variable Tutte polynomial the author has associated with a morphism of matroids, more precisely with a matroid strong map, or matroid perspective in the present paper, or, equivalently by the Factorization Theorem, with a matroid together with a distinguished subset of elements. Most algebraic properties of the usual 2-variable Tutte polynomial of a matroid generalize to the 3-variable polynomial. Among specific properties we show that the 3-variable...

Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes

Bruno Courcelle, Frédéric Olive (1999)

Annales de l'institut Fourier

Nous définissons une structure logique permettant de représenter les classes d’homéomorphismes des arrangements de pseudodroites du plan euclidien. Nous donnons une axiomatisation finie du premier ordre de la réalisabilité des arrangements de pseudodroites.

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