6 papers
Dense sets without large sumsets
Gabriel Dahia, João Pedro Marciano, Victor Souza
We prove, for all fixed , and all sufficiently large , that there exists with such that for all ${A, B \subset \mat…
The sandglass conjecture beyond cancellative pairs
Adva Mond, Victor Souza, Leo Versteegen
The sandglass conjecture, posed by Simonyi, states that if a pair of families of subsets of is recovering then . We improve the best known upper bo…
On problems in extremal multigraph theory
Victor Falgas-Ravry, Adva Mond, Rik Sarkar +1
A multigraph G is said to be an (s,q)-graph if every s-set of vertices in G supports at most q edges (counting multiplicities). In this paper we consider the maximal sum and produc…
Intersections of random chords of a circle
Cynthia Bortolotto, Victor Souza
Where are the intersection points of diagonals of a regular -gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate the…
The Maker-Breaker percolation game on a random board
Vojtěch Dvořák, Adva Mond, Victor Souza
The Maker-Breaker percolation game on , introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{…
On the number of monochromatic solutions to multiplicative equations
Lucas Aragão, Jonathan Chapman, Miquel Ortega +1
The following question was asked by Prendiville: given an -colouring of the interval , what is the minimum number of monochromatic solutions of the equation $x…