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On the orbits associated with the Collatz conjecture. / Kauffman, Louis H.; Lopes, Pedro.
в: Linear Algebra and Its Applications, Том 615, 15.04.2021, стр. 143-154.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On the orbits associated with the Collatz conjecture
AU - Kauffman, Louis H.
AU - Lopes, Pedro
N1 - Funding Information: Kauffman's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation).Lopes acknowledges support from FCT (Funda??o para a Ci?ncia e a Tecnologia), Portugal, through project FCT PTDC/MAT-PUR/31089/2017, ?Higher Structures and Applications?. Publisher Copyright: © 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/4/15
Y1 - 2021/4/15
N2 - This article is based upon previous work by Sousa Ramos and his collaborators. They first prove that the existence of only one orbit associated with the Collatz conjecture is equivalent to the determinant of each matrix of a certain sequence of matrices to have the same value. These matrices are called Collatz matrices. The second step in their work would be to calculate this determinant for each of the Collatz matrices. Having calculated this determinant for the first few terms of the sequence of matrices, their plan was to prove the determinant of the current term equals the determinant of the previous one. They could not prove it for the cases where the dimensions of the matrices are 26+54l or 44+54l, where l is a positive integer. In the current article we improve on these results.
AB - This article is based upon previous work by Sousa Ramos and his collaborators. They first prove that the existence of only one orbit associated with the Collatz conjecture is equivalent to the determinant of each matrix of a certain sequence of matrices to have the same value. These matrices are called Collatz matrices. The second step in their work would be to calculate this determinant for each of the Collatz matrices. Having calculated this determinant for the first few terms of the sequence of matrices, their plan was to prove the determinant of the current term equals the determinant of the previous one. They could not prove it for the cases where the dimensions of the matrices are 26+54l or 44+54l, where l is a positive integer. In the current article we improve on these results.
KW - Collatz conjecture
KW - Determinants
KW - Permutations
KW - Recurrence
UR - http://www.scopus.com/inward/record.url?scp=85099391478&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2020.12.031
DO - 10.1016/j.laa.2020.12.031
M3 - Article
AN - SCOPUS:85099391478
VL - 615
SP - 143
EP - 154
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -
ID: 27645798