Francesco Monopoli

collaborators

4 papers

math.NT2015

Minimizing the frequency of carries in modular addition

Francesco Monopoli

When adding integers in base $m$ , carries occur. The same happens modulo a generic integer $q$ when the set of digits is a complete set of residues modulo $m$ for some positive int…

math.NT2015

Carries and the arithmetic progression structure of sets

Francesco Monopoli, Imre Z. Ruzsa

If we want to represent integers in base $m$ , we need a set $A$ of digits, which needs to be a complete set of residues modulo $m$ . When adding two integers with last digits $a_1,…

math.NT2015

A generalization of sumsets modulo a prime

Francesco Monopoli

Let $A$ be a set in an abelian group $G$ . For integers $h, r \geq 1$ the generalized $h$ -fold sumset, denoted by $h^{(r)} A$ , is the set of sums of $h$ elements of $A$ , where each el…

math.CO2014

Absolute differences along Hamiltonian paths

Francesco Monopoli

Given a set $A$ of real numbers consider the complete graph on the elements of $A$ . We prove that if $A$ is an arithmetic progression then for every vertex $a \in A$ there exists an…