Line Percolation in Finite Projective Planes

Line Percolation in Finite Projective Planes

We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the minimal and maximal percolation time as well as on the critical probability in the projective plane are also presented.

Transitive hyperovals in finite projective planes

Special Point Sets in Finite Projective Planes

We consider the following three problems: 1. Let U be a q-subset of GF(q 2) with the properties 0; 1 2 U and u ? v is a square for all u; v 2 U. Does it follow that U consists of the elements of the subbeld GF(q)? Here q is odd. 2. Let f : GF(q) ! GF(q) be any function, and let be the set of diierence quotients (directions, slopes). What are the possibilities for jD f j? 3. Let B be a subset of...

Frobenius Collineations in Finite Projective Planes

of order n on V . It follows that R induces a projective collineation φ on the (n−1)dimensional projective space PG(n−1, q). We call φ and any projective collineation conjugate to φ a Frobenius collineation. In the present paper we shall study the case n = 3, that is, the Frobenius collineations of the projective plane PG(2, q). Let P = PG(2, q). Then every Singer cycle σ (see Section 3) of P d...

Efficient Imbeddings of Finite Projective Planes

We use index-one voltage graph imbeddings of Cayley graphs (Cayley maps) for the groups Zn2+n + v where n is a prime power, to depict the finite projective planes PG(2, n). Subject to the condition that Zn2+n + i act regularly not only on the images of the points and of the lines of PG(2, n), but also on each orbit of the region set for the imbedding, the imbeddings constructed have maximum eff...