Reorienting regular n-gons

Joseph A Gallian; Charles A. Marttila

doi:10.1007/BF02190498

Reorienting regular n-gons

Joseph A Gallian
, Charles A. Marttila

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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, ..., a_n from G such that G={e, a₁, a₁a₂, ..., a₁a₂ ... a_n}). 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.

Original language	English (US)
Pages (from-to)	97-103
Number of pages	7
Journal	Aequationes Mathematicae
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/BF02190498
State	Published - Dec 1980

Keywords

AMS (1970) subject classification: Primary 05A15, 20F05

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10.1007/BF02190498

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abstract = "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.",

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AU - Marttila, Charles A.

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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

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JO - Aequationes Mathematicae

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ER -

Reorienting regular n-gons

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