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Mat. Zametki, 2016, Volume 100, Issue 2, Pages 196–211 (Mi mz10626)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Additive Complexity of GCD and LCM Matrices

S. B. Gashkova, I. S. Sergeevb

a Lomonosov Moscow State University
b Research Institute "Kvant"

Abstract: In the paper, the additive complexity of matrices formed by positive integer powers of greatest common divisors and least common multiples of the indices of the rows and columns is considered. It is proved that the complexity of the $n\times n$ matrix formed by the numbers $GCD^r(i,k)$ over the basis $\{x+y\}$ is asymptotically equal to $rn \log_2 n$ as $n\to\infty$, and the complexity of the $n\times n$ matrix formed by the numbers $LCM^r(i,k)$ over the basis $\{x+y,-x\}$ is asymptotically equal to $2rn \log_2 n$ as $n\to \infty$.

Keywords: greatest common divisor, least common multiple, additive complexity of matrices, Smith determinant, circuit complexity.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00671а
This work was financially supported by the Russian Foundation for Basic Research under grant 14-01-00671a.


DOI: https://doi.org/10.4213/mzm10626

Full text: PDF file (568 kB)
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English version:
Mathematical Notes, 2016, 100:2, 199–212

Bibliographic databases:

UDC: 519.714+511.17
Received: 24.09.2014

Citation: S. B. Gashkov, I. S. Sergeev, “On the Additive Complexity of GCD and LCM Matrices”, Mat. Zametki, 100:2 (2016), 196–211; Math. Notes, 100:2 (2016), 199–212

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Han H., Li Q., Wen Y., Wen Sh., Li J., “Generalization of Gcd Matrices”, Evol. Intell.  crossref  isi
    2. H. Han, “Port area distribution and marine economic prediction based on Kronecker direct-product of the meet-matrix”, J. Coast. Res., 2020, no. 103, 780–783  crossref  isi
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