On the maximal sum of the entries of a matrix power
Year: 2024
Type: article
Abstract: Let pn be the maximal sum of the entries of A2, where A is a square matrix of size n, consisting of the numbers 1, 2, …, n2, each appearing exactly once. We prove that pn = Θ(n7). More precisely, we show that n(240n6 + 28n5 + 364n4 + 210n2 − 28n + 26 − 105((−1)n + 1))/840 ≤ pn ≤ n3(n2 + 1)(7n2 + 5)/24.
Authors: Sela Fried, Toufik Mansour
Institution: University of Haifa
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403836331