On the maximal sum of the entries of a matrix power

Sela Fried; Toufik Mansour

doi:10.26493/2590-9770.1682.fe2

On the maximal sum of the entries of a matrix power

Sela Fried, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let p_n 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 p_n = Θ(n⁷). More precisely, we show that n(240n⁶ + 28n⁵ + 364n⁴ + 210n² − 28n + 26 − 105((−1)ⁿ + 1))/840 ≤ p_n ≤ n³(n² + 1)(7n² + 5)/24.

Original language	English
Journal	Art of Discrete and Applied Mathematics
Volume	7
Issue number	3
DOIs	https://doi.org/10.26493/2590-9770.1682.fe2
State	Published - 2024

Bibliographical note

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© 2024 University of Primorska. All rights reserved.

Keywords

Matrix power
maximal entries sum

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.26493/2590-9770.1682.fe2

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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.",

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AB - 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.

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On the maximal sum of the entries of a matrix power

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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