30 citations · 73 across the 25 of their papers we have counts for
9 papers · 1 filter
Ratio sets of random sets
Javier Cilleruelo, Jorge Guijarro-Ordonez
We study the typical behavior of the size of the ratio set for a random subset . For example, we prove that $|A/A|\sim \frac{2\text{Li}_2(3/4)}{π^2}…
Sidon set systems
Javier Cilleruelo, Oriol Serra, Maximilian Wötzel
A family of -subsets of is a Sidon system if the sumsets , are pairwise distinct. We show that the largest cardinalit…
Visible lattice points and the chromatic zeta function of a graph
Javier Cilleruelo
We study the probability that a cycle of length k in the lattice [1, n]^s does not contain more lattice points than the k vertices of the cycle. Then we generalize this problem to…
Elementary methods for incidence problems in finite fields
Javier Cilleruelo, Alex Iosevich, Ben Lund +2
We use elementary methods to prove an incidence theorem for points and spheres in . As an application, we show that any point set of with…
Infinite graphs that do not contain cycles of length four
Javier Cilleruelo
We construct a countable infinite graph G that does not contain cycles of length four having the property that the sequence of graphs induced by the first vertices has mi…
An extremal problem on Hilbert cubes and complete r-partite hypergraphs
Javier Cilleruelo
We construct a set of positive integers A in {1,..., n} with |A|>> n^{2/3} that does not contain Hilbert cubes of dimension 3. As a consequence we prove that ex(n; K^(3)(2,2,2))>>…