30 citations · 41 across the 10 of their papers we have counts for
5 papers · 2 filters
On the solutions to a power sum problem
Johan Andersson
In a recent paper we proved that if (*)=\inf_{|z_k|=1}\max_{v=1,...,n^2-n} |\sum_{k=1}^n z_k^v|, then (*)=\sqrt{n-1} if n-1 is a prime power. We proved that a construction of Fabry…
Turan's problem 10 revisited
Johan Andersson
In this paper we prove that inf_{|z_k| => 1} max_{v=1,...,n^2} |sum_{k=1}^n z_k^v| = sqrt n+O(n^{0.2625+epsilon}). This improves on the bound O(sqrt (n log n)) of Erdos and Renyi.…
On the number of plane partitions and non isomorphic subgroup towers of abelian groups
Johan Andersson, Jan Snellman
We study the number of plane partitions, weighted on the sum of the first row. Using Erhart reciprocity, we prove an identity for the generating function. For the spec…
Explicit solutions to certain inf max problems from Turan power sum theory
Johan Andersson
Let s_v denote the pure power sum \sum_{k=1}^n z_k^v. In a previous paper we proved that \sqrt n <= \inf_{|z_k| => 1} \max_{v=1,...,n^2} |s_v| <= \sqrt{n+1} when n+1 is prime. In t…
On Factorisations of Matrices and Abelian Groups
Johan Andersson, Gautami Bhowmik
We establish correspondances between factorisations of finite abelian groups (direct factors, unitary factors, non isomorphic subgroup classes) and factorisations of integer matric…