Finite spherical geometries
Flag-transitive extensions of dual affine spaces.
Forbidden-minor characterization for the class of cographic element splitting matroids
In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M(K₄).
Forbidden-minor characterization for the class of graphic element splitting matroids
This paper is based on the element splitting operation for binary matroids that was introduced by Azadi as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which graphic matroids M have the property that the element splitting operation, by every pair of elements on M yields a graphic matroid. This problem is solved by proving that there is exactly one minor-minimal matroid that does not have this property.
Fractal Penrose tiles II: Tiles with fractal boundary as duals of Penrose triangles.
Fractal representation of the attractive lamination of an automorphism of the free group
In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers (iwip) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination...
Frankl’s conjecture for large semimodular and planar semimodular lattices
A lattice is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element such that at most half of the elements of satisfy . Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let denote the number of nonzero join-irreducible elements of . It is well-known that consists of at most elements....
Free objects in the category of geometries.
Frequency squares and affine designs.
From a 1-rotational RBIBD to a partitioned difference family.
From Covering Designs to Graphs.
Further Results Concerning the Existence of Handcuffed Designs.