Korean J. Math. Vol. 26 No. 2 (2018) pp.167-174
DOI: https://doi.org/10.11568/kjm.2018.26.2.167

Polygonal partitions

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Published: Jun 30, 2018
Keywords:
Partitions, group action, partition congruence
Mathematics Subject Classification:
11P83

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Byungchan Kim
School of Liberal Arts Seoul National University of Science and Technology Seoul, 01811, Korea

Abstract

By acting the dihedral group $D_{k}$ on the set of $k$-tuple multi-partitions, we introduce $k$-gonal partitions for all positive integers $k$. We give generating functions for these new partition functions and investigate their arithmetic properties.



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Supporting Agencies

This study was supported by the Research Program funded by the SeoulTech (Seoul National University of Science and Technology).

References

[1] B. Kim, Group Actions on Partitions, Elect. J. Comb. 24 (2017), Paper #P3.58. Google Scholar

[2] G. Ligozat, Courbes modulaires de genre 1, Soci et e Math ematique de France, Paris, 1975, Bull. Soc. Math. France, M em. 43, Suppl ement au Bull. Soc. Math. France Tome 103, no. 3. Google Scholar

[3] M. Newman, Construction and application of a class of modular functions II, Proc. London Math. Soc. (3) 9 (1959), 373–387. Google Scholar

[4] K. Ono, Web of Modularity: arithmetic of the coefficients of modular forms and q-series, CBMS Regional Conference Series in Mathematics, 102. Published for the Conference Board of the Mathematical Sciences, Washington, DC, by the American Mathematical Society, Providence, RI, 2004. Google Scholar