Squeezing the Accordion in a Strongly n-Uniform Hjelmslev Plane.
Standard monomials for q-uniform families and a conjecture of Babai and Frankl
Let n, k, α be integers, n, α>0, p be a prime and q=p α. Consider the complete q-uniform family We study certain inclusion matrices attached to F(k,q) over the field . We show that if l≤q−1 and 2l≤n then This extends a theorem of Frankl [7] obtained for the case α=1. In the proof we use arguments involving Gröbner bases, standard monomials and reduction. As an application, we solve a problem of Babai and Frankl related to the size of some L-intersecting families modulo q.
Steiner Systems which Admit Block Transitive Automorphism Groups of Small Rank.
Steiner triple systems and existentially closed graphs.
Steiner triple systems intersecting in pairwise disjoint blocks.
Steinhaus chessboard theorem
Strictly balanced submatroids in random subsets of projective geometries
Strongly n-Uniform and Level n-Hjelmslev Planes.
Strongly regular locally -graphs.
Subdeterminants and subgraphs
Subfield permutation polynomials and orthogonal subfield systems in finite fields
Sublattices of certain Coxeter lattices
In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.
Subplane replacement in projective planes.
Subsets of the unit ball the are separated by more than one
Substitutions, abstract number systems and the space filling property
In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.
Succession rules and deco polyominoes
Succession rules and Deco polyominoes
In this paper, we examine the class of "deco" polyominoes and the succession rule describing their construction. These polyominoes are enumerated according to their directed height by factorial numbers. By changing some aspects of the "factorial" rule, we obtain some succession rules that describe various "deco" polyomino subclasses. By enumerating the subclasses according to their height and width, we find the following well-known numbers: Stirling numbers of the first and second kind,...
Sulla famiglia dei flocks lineari di una quadrica iperbolica assolutamente irriducibile di uno spazio proiettivo finito
In questa Nota diamo una caratterizzazione dell'insieme di tutti i flocks lineari della quadrica iperbolica assolutamente irriducibile in .
Summaries of articles published in this issue
Sunflowers in lattices.