Squares of Q sets

Borel Sets with Large Squares

For a cardinal μ we give a sufficient condition ⊕μ (involving ranks measuring existence of independent sets) for: ⊗μ: if a Borel set B ⊆ R × R contains a μ-square (i.e. a set of the form A × A, |A| = μ) then it contains a 20 -square and even a perfect square. And also for ⊗′μ: if ψ ∈ Lω1,ω has a model of cardinality μ then it has a model of cardinality continuum generated in a “nice”, “absolute...

Block Transitive Meager Squares over GF (q) for prime q

This paper shows the existence of a class of block transitive meager squares of order q on GF (q) for odd prime q, q large. Using these meager squares along with other known meager system constructions, we determine the spectrum of orders that admit meager systems: all odd n, n ≥ 9. Using this result, it is also determined that the spectrum of orders that admit 5-sparse Steiner triple systems i...

Maximal sets of mutually orthogonal Latin squares

Maximal sets of s mutually orthogonal Latin squares of order v are constructed for in nitely many new pairs (s; v). c © 1999 Published by Elsevier Science B.V. All rights reserved

Bounds on squares of two-sets

The size of minimal blocking sets of Q(4, q)

Let Q(2n+2, q) denote the non-singular parabolic quadric in the projective geometry PG(2n+2, q). We describe the implementation in GAP of an algorithm to determine the minimal number of points of a minimal blocking set of Q(4, q), for q = 5, 7