TY - JOUR
T1 - Reorienting regular n-gons
AU - Gallian, Joseph A
AU - Marttila, Charles A.
PY - 1980/12
Y1 - 1980/12
N2 - Imagine that randomly oriented objects in the shape of a regular n-sided polygon are moving on a conveyor. Our aim is to specify sequences composed of two different rigid motions which, when performed on these objects, will reposition them in all possible ways. We call such sequences facing sequences. (Expressed in group theoretical terms, a facing sequence in a group G is a sequence of elements a1, a2, ..., an from G such that G={e, a1, a1a2, ..., a1a2 ... an}). In this paper we classify various kinds of facing sequences and determine some of their properties. The arguments are group theoretical and combinatorial in nature.
AB - Imagine that randomly oriented objects in the shape of a regular n-sided polygon are moving on a conveyor. Our aim is to specify sequences composed of two different rigid motions which, when performed on these objects, will reposition them in all possible ways. We call such sequences facing sequences. (Expressed in group theoretical terms, a facing sequence in a group G is a sequence of elements a1, a2, ..., an from G such that G={e, a1, a1a2, ..., a1a2 ... an}). In this paper we classify various kinds of facing sequences and determine some of their properties. The arguments are group theoretical and combinatorial in nature.
KW - AMS (1970) subject classification: Primary 05A15, 20F05
UR - http://www.scopus.com/inward/record.url?scp=34250249198&partnerID=8YFLogxK
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U2 - 10.1007/BF02190498
DO - 10.1007/BF02190498
M3 - Article
AN - SCOPUS:34250249198
SN - 0001-9054
VL - 20
SP - 97
EP - 103
JO - Aequationes Mathematicae
JF - Aequationes Mathematicae
IS - 1
ER -