Applications of Polya’s Enumeration Formula
DOI:
https://doi.org/10.61173/3vz18a53Keywords:
Polya’s Enumeration Theorem, Cycle Index, Isomers, Simple Graph, ChordAbstract
This essay purely aims to provide basic information related to Polya’s Enumeration Theorem and its applications in three distinct fields: Chemistry, Music, and Simple graph. Each section access the theorem in various insights and perspectives, resulting in a mix of ideas without strictly deeper focus.
References
De Wet, P. (2000). Constructing a Large Number of Nonisomorphic Graphs of Order n. [online] Morehead Electronic Journal of Applicable Mathematics Issue. Available at: https://scholarworks.moreheadstate.edu/cgi/ viewcontent.cgi?article=1004&context=mejam_archives [Accessed 27 Aug. 2024].
Gatt, V. (2013). On the Enumeration of Circulant Graphs of Prime-Power Order: the case of p 3. [online] Available at: https://arxiv.org/pdf/1703.06038 [Accessed 27 Aug. 2024].
Harald Fripertinger (1999). Enumeration of mosaics. 199(1-3), pp.49–60. doi:https://doi.org/10.1016/s0012- 365x(98)00285-4.
Jin, J. (2018). Analysis and Applications of Burnside’s Lemma. [online] Available at: https://math.mit.edu/~apost/ courses/18.204_2018/Jenny_Jin_paper.pdf. 4. Conclusions Keller, M.T. and Trotter, W.T. (n.d.). AC Applications of Based on the following, we can conclude that: Pólya’s Enumeration Formula. [online] rellek.net. Avail- 1) The number of specific isomers can be counted using able at: https://rellek.net/book/s_polya_apps.html.
Polya’s enumeration theorem. Matamala, A.R. (2002). PÓLYA’S COMBINATORIAL 2)Polya’s enumeration theorem can enumerate the number METHOD AND THE ISOMER ENUMERATION PROB- of chords with k notes in a typical 12-note scale. LEM. Boletín de la Sociedad Chilena de Química, 47(2). 3)Polya’s enumeration theorem can count non-isomorphic doi:https://doi.org/10.4067/s0366-16442002000200006. graphs with n vertices. Pólya’s Enumeration Theorem. (n.d.). Available at: https:// Overall, Polya’s theorem streamlines complex counting feog.github.io/chap1dm.pdf. tasks by leveraging symmetry and rotation, making it a valuable tool in these diverse areas.
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