On the maximal sum of the entries of a matrix power
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
- Toufik Mansour (ORCID: https://orcid.org/0000-0001-8028-2391)
- Sela Fried (ORCID: https://orcid.org/0000-0002-1547-4925)
Institutions
- University of Haifa (IL)
Publication Details
- Journal
- The Art of Discrete and Applied Mathematics
- Published
- 2024-10-28
- DOI
- https://doi.org/10.26493/2590-9770.1682.fe2
- Citations
- 1
- Primary Topic
- graph theory and CDMA systems
- Type
- article
- Field-Weighted Citation Impact
- 0.21