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Zapiski Nauchnykh Seminarov POMI, 2003, Volume 302, Pages 188–197 (Mi znsl933)  
This article is cited in 9 scientific papers (total in 9 papers)

The number of words of a given length in the planar crystallographic groups

A. V. Shutov

Vladimir State Pedagogical University
Full-text PDF (199 kB) Citations (9)
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Abstract: This paper reveals an interrelation between the words in groups and the growth process of the corresponding graphs, based on which exact formulas for the number of words of a given length for all 17 planar crystallographic groups are obtained. Sloane's conjecture on the graphs of these groups is proved.
Received: 12.09.2003
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 129, Issue 3, Pages 3922–3926
DOI: https://doi.org/10.1007/s10958-005-0329-2
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: A. V. Shutov, “The number of words of a given length in the planar crystallographic groups”, Analytical theory of numbers and theory of functions. Part 19, Zap. Nauchn. Sem. POMI, 302, POMI, St. Petersburg, 2003, 188–197; J. Math. Sci. (N. Y.), 129:3 (2005), 3922–3926
Citation in format AMSBIB
\Bibitem{Shu03}
\by A.~V.~Shutov
\paper The number of words of a~given length in the planar crystallographic groups
\inbook Analytical theory of numbers and theory of functions. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 302
\pages 188--197
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl933}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2023041}
\zmath{https://zbmath.org/?q=an:1144.20314}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 129
\issue 3
\pages 3922--3926
\crossref{https://doi.org/10.1007/s10958-005-0329-2}
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  • https://www.mathnet.ru/eng/znsl/v302/p188
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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