Carlo Sanna

activity

20242026

collaborators

5 papers

math.CO2026

Counting contiguous superregular $4 \times 4$ matrices

Carlo Sanna

This short paper has two goals. First, explaining a simple procedure (which is essentially folklore) that, sometimes, makes it possible to obtain a formula for the number of soluti…

math.NT2026

Another factor of integer polynomials with minimal integrals

Alice Bazzanella, Carlo Sanna

Let $N$ be a positive integer and let $S_{N}$ be the set of polynomials with integer coefficients, degree less than $N$ , and minimal positive integral over $[0, 1]$ . D. Bazzanella ini…

math.NT2026

Explicit inequalities for the nth lucky number

Carlo Sanna

Gardiner, Lazarus, Metropolis, and Ulam introduced a variation of the sieve of Eratosthenes that (instead of producing the sequence of prime numbers) produces the sequence of "luck…

math.NT2025

A lower bound for the number of Egyptian fractions

An Egyptian fraction is a sum of the form $1/ n_{1} + \dots + 1/ n_{r}$ where $n_{1}, \dots, n_{k}$ are distinct positive integers. We prove explicit lower bounds for the cardinality of the…

math.CO2024

On the number of solutions to a random instance of the permuted kernel problem

Carlo Sanna

The Permuted Kernel Problem (PKP) is a problem in linear algebra that was first introduced by Shamir in 1989. Roughly speaking, given an $ℓ \times m$ matrix $A$ and an…

Counting contiguous superregular 4×4 matrices

Another factor of integer polynomials with minimal integrals

Explicit inequalities for the nth lucky number

A lower bound for the number of Egyptian fractions

On the number of solutions to a random instance of the permuted kernel problem

Counting contiguous superregular $4 \times 4$ matrices