16 citations · 33 across the 22 of their papers we have counts for
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A characterization of polynomials whose high powers have non-negative coefficients
Marcus Michelen, Julian Sahasrabudhe
Let be a polynomial with real coefficients. We say that is eventually non-negative if has non-negative coefficients for all sufficiently large $m \i…
Central limit theorems and the geometry of polynomials
Marcus Michelen, Julian Sahasrabudhe
Let be a random variable, with mean and standard deviation and let \[f_X(z) = \sum_{k} \mathbb{P}(X = k) z^k, \] be its probability generating funct…
Flat Littlewood Polynomials Exist
Paul Balister, Béla Bollobás, Robert Morris +2
We show that there exist absolute constants such that, for all , there exists a polynomial of degree , with coefficients, such that $$δ\sqrt…
The structure and number of Erdős covering systems
Paul Balister, Béla Bollobás, Robert Morris +2
Introduced by Erdős in 1950, a covering system of the integers is a finite collection of arithmetic progressions whose union is the set . Many beautiful questions and c…
The Erdős-Selfridge problem with square-free moduli
Paul Balister, Béla Bollobás, Robert Morris +2
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erdős in…