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Title: Symmetry of iteration graphs (English)
Author: Carlip, Walter
Author: Mincheva, Martina
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 1
Year: 2008
Pages: 131-145
Summary lang: English
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Category: math
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Summary: We examine iteration graphs of the squaring function on the rings $\mathbb{Z}/n\mathbb{Z}$ when $n = 2^{k}p$, for $p$ a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when $k=3$ and when $k\ge 5$ and are symmetric when $k = 4$. (English)
Keyword: digraph
Keyword: iteration digraph
Keyword: quadratic map
Keyword: tree
Keyword: cycle
MSC: 05C20
MSC: 05C62
MSC: 11T99
idZBL: Zbl 1174.05048
idMR: MR2402530
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Date available: 2009-09-24T11:54:02Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128250
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Reference: [5] Thomas D. Rogers: The graph of the square mapping on the prime fields.Discrete Math. 148 (1996), 317–324. MR 1368298, 10.1016/0012-365X(94)00250-M
Reference: [6] Lawrence Somer and Michal Křížek: On a connection of number theory with graph theory.Czechoslovak Math. J. 54 (2004), 465–485. MR 2059267, 10.1023/B:CMAJ.0000042385.93571.58
Reference: [7] L. Szalay: A discrete iteration in number theory.BDTF Tud. Közl. 8 (1992), 71–91. Zbl 0801.11011
Reference: [8] Troy Vasiga and Jeffrey Shallit: On the iteration of certain quadratic maps over $\text{GF}(p)$.Discrete Math. 277 (2004), 219–240. MR 2033734
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