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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2003 Volume 302, Pages 188–197 (Mi znsl933)

This article is cited in 9 papers

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

A. V. Shutov

Vladimir State Pedagogical University

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.

UDC: 519.21

Received: 12.09.2003


 English version:
Journal of Mathematical Sciences (New York), 2005, 129:3, 3922–3926

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