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Coset decompositions of space groups: applications to domain structure analysis. (English) Zbl 1188.20050

Summary: Left- and double-coset decompositions of space groups are systematically analysed by putting the emphasis on the introduction of special auxiliary groups. An algorithm is tailored to exploit the specific structure of space groups. The new results are, amongst others, an efficient alternative method to determine for space groups minimal sets of double-coset representatives and a general formula that gives the structure and number of left cosets that are contained in double cosets. Left-coset and double-coset decompositions of space groups are exploited in domain structure analysis.

MSC:

20H15 Other geometric groups, including crystallographic groups
82D25 Statistical mechanics of crystals
82-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics
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