FITA FATMAWATI, (1327031007) (2016) CYCLE INDEX POLYNOMIAL, TEOREMA POLYA DAN TERAPANNYA PADA ENUMERASI POLA WARNA OKTAHEDRON. Masters thesis, Universitas Lampung.
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Abstract
Salah satu permasalahan dalam Teori Grup adalah masalah enumerasi. Masalah enumerasi dapat diselesaikan salah satunya dengan Teorema Polya. Teorema Polya berkaitan dengan cycle index polynomial suatu grup, karena Teorema Polya merupakan teorema yang digunakan untuk menghitung banyaknya pola-pola suatu grup permutasi yang membentuk cycle index grup tersebut. Teorema Polya terdiri dari Teorema Polya I dan Teorema Polya II. Tujuan penelitian ini adalah mencari banyaknya pola warna oktahedron dengan menggunakan Teorema Polya. Dari penelitian didapat hasil bahwa jumlah pola warna yang berbeda pada titik-titik oktahedron untuk penggunaan 1 sampai 6 warna yaitu, 1, 10, 57, 240, 800 dan 2.226 pola warna. Untuk pewarnaan pada garis-garis oktahedron diperoleh jumlah pola warna yang berbeda dengan penggunaan 1 sampai 12 warna yaitu : 1, 218, 22.815, 703.760, 10.194.250, 90.775.566, 576.941.778, 2.863.870.080, 11.769.161.895, 41.669.295.250, 130.772.947.481, 371.513.523.888 pola warna. Sedangkan jumlah pola warna yang berbeda pada pewarnaan bidang-bidang oktahedron yaitu : 1, 23, 333, 2.916, 16.725, 70.911, 241.913, 701.968 pola warna. Kata kunci : Teori Grup, Teorema Polya, Cycle Index Polynomial abstract One of the problem involved in Group Theory is the enumeration problem. This problem can be solved by Polya’s Theorem. Polya’s theorem closely related to the cycle index polynomial of a group, because it used to count the number of patterns on permutations group that form the cycle index of groups. The Polya’s Theorem consists of Polya’s Theorem I and Polya’s Theorem II. The aim of this observation is to find the number of patterns of coloured octahedron using the Polya’s Theorem. The result show that the number of patterns of coloured points of octahedron for 1 to 6 colours are : 1, 10, 57, 240, 800 and 2.226 colour patterns. The number of patterns of coloured lines of octahedron for 1 to 12 colours are : 1, 218, 22.815, 703.760, 10.194.250, 90.775.566, 576.941.778, 2.863.870.080, 11.769.161.895, 41.669.295.250, 130.772.947.481, and 371.513.523.888 colour patterns, while the number of patterns of coloured sides of octahedron for 1 to 8 colours are : 1, 23, 333, 2.916, 16.725, 70.911, 241.913, and 701.968 colour patterns. Keyword : Group Theory, Polya’s Theorem, Cycle Index Polynomial
| Item Type: | Thesis (Masters) |
|---|---|
| Subjects: | Q Science (General) > QA Mathematics |
| Divisions: | Fakultas MIPA > Prodi Magister Ilmu Matematika |
| Depositing User: | 8016107 . Digilib |
| Date Deposited: | 26 Jan 2016 06:58 |
| Last Modified: | 26 Jan 2016 06:58 |
| URI: | http://digilib.unila.ac.id/id/eprint/20567 |
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