Application of a permutation group on sasirangan pattern

https://doi.org/10.24042/djm.v4i3.10338

Na'imah Hijriati, Dewi Sri Susanti, Raihan Nooriman, Geofani Setiawan

Abstract

A permutation group is a group of all permutations of some set. If the set that forms a permutation group is the n-first of natural number, then a permutation group is called a symmetry group. There is another type of group, i.e., a cyclic group and a dihedral group, and they are a subgroup of a symmetry group by numbering the vertices of the polygon. Sasirangan is the traditional batik from the South Kalimantan. There are 18 traditional patterns. All the patterns make some polygon. Because of this, the purpose of this research is to investigate the type of group that forms the patterns of Sasirangan. First, the authors give the procedure to investigate the patterns of Sasirangan, then use that procedure to the patterns of Sasirangan. The result of this research is the patterns of Sasirangan form cyclic groups C_1  and C_2, and dihedral groups D_2, D_4, D_5 and D_8.

Keywords

Permutation Group; Cyclic Group; Symmetry Group; Dihedral Group; Sasirangan.

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DOI: https://doi.org/10.24042/djm.v4i3.10338

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