7 papers
Counting contiguous superregular 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…
Another factor of integer polynomials with minimal integrals
Alice Bazzanella, Carlo Sanna
Let be a positive integer and let be the set of polynomials with integer coefficients, degree less than , and minimal positive integral over . D. Bazzanella ini…
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…
A lower bound for the number of Egyptian fractions
Sandro Bettin, Loïc Grenié, Giuseppe Molteni +1
An Egyptian fraction is a sum of the form where are distinct positive integers. We prove explicit lower bounds for the cardinality of the…
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 matrix and an…
Counting numbers that are divisible by the product of their digits
Qizheng He, Carlo Sanna
Let be a positive integer. A natural number is said to be a base- Zuckerman number if it is divisible by the product of its base- digits. Let be…
On the number of residues of certain second-order linear recurrences
Federico Accossato, Carlo Sanna
For every monic polynomial with , let be the set of all linear recurrences with values in and char…