Tableaux in the Whitney module of a matroid.
The active bijection between regions and simplices in supersolvable arrangements of hyperplanes.
The cones associated to some tranversal polymatroids.
The contributions of Hilbert and Dehn to non-archimedean geometries and their impact on the italian school
In this paper we investigate the contribution of Dehn to the development of non-Archimedean geometries. We will see that it is possible to construct some models of non-Archimedean geometries in order to prove the independence of the continuity axiom and we will study the interrelations between Archimedes’ axiom and Legendre’s theorems. Some of these interrelations were also studied by Bonola, who was one of the very few Italian scholars to appreciate Dehn’s work. We will see that, if Archimedes’...
The middle graph of a hypergraph
The toric ideal of a matroid of rank 3 is generated by quadrics.
The tree of life and other affine buildings.
The Tutte group of projective spaces.
The Tutte polynomial of a morphism of matroids I. Set-pointed matroids and matroid perspectives
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...
The vanishing of the cohomology of the Orlik-Solomon algebras.
Topological Representation of Dual Pairs of Oriented Matroids.
Transversal and cotransversal matroids via their representations.
Transversal lattices.
Two analogues of a classical sequence.
Two Constructions of Oriented Matroids with Disconnected Extension Space.
Two interesting oriented matroids.