Article Per Year (5 Year)
p-Index From 2020 - 2025
0.23
P-Index
This Author published in this journals
All Journal Journal of Mathematics Theory and Applications
Anggelica Yunita Liu
Unknown Affiliation
Computer Science & IT Decision Sciences, Operations Research & Management Education Health Professions Immunology & microbiology

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
Aplikasi Teorema Polya dalam Menentukan Banyaknya Cara Pewarnaan Permukaan Oktahedron dengan m-Warna Anggelica Yunita Liu; Nugraha Dethan; Fitriani
Journal of Mathematics Theory and Applications Vol. 3 No. 2 (2025): Edisi April 2025
Publisher : Program Studi Matematika, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/j-math.v3i2.9456

Abstract

One application of the permutation group concept is related to solving enumeration problems and one method that can solve this problem is Polya's Theorem. Polya's theorem is a calculation technique that combines abstract algebraic structures with combinatorics and can be used to calculate objects in permutation groups. A regular octahedron is an octahedron composed of eight equilateral triangles and the four sides of the octahedron meet at each vertex and have twelve edges. In 2015, research was carried out on the many ways to color the surface of a cube with m-colors. This research aims to determine the number of ways to color the surface of an octahedron with m-colors by using the Polya theorem and permutation groups to determine the rotational symmetry group formed by the octahedron as well as the number of cycle indices formed from each element in the rotational symmetry group itself. Based on the research results, it is obtained that the rotational symmetry group formed by the octahedron is S_4 and the number of cycle indices of the octahedron permutation group is Z(G) = 1/24*(x_1^8+6x_4^2+9x_2^4+8x_1^2*x_3^2) . After substituting the symmetry index and cycle index into the Polya theorem formula, we can conclude that the number of ways to color the octahedron surface with m-colors is 1/24*(m^8+17m^4+6m^2).
Co-Authors Fitriani Nugraha Dethan