Arithmagons and Geometrically Invariant Multiplicative Integer Partitions
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Abstract
In this article, we introduce a formal denition for integral arithmagons. Informally, an integral arithmagon is a polygonal gure with integer labeled vertices and edges in which, under a binary operation, adjacent vertices equal the included edge. By considering the group of automorphisms for the associated graph, we count the number of integral arithmagons whose exterior sum or product equals a xed number.
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Franco, J., Champion, J., & Lyons, J.
(2016).
Arithmagons and Geometrically Invariant Multiplicative Integer Partitions.
Acta Mathematica Universitatis Comenianae, 85(1), 87-95.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/140/284
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References
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[2] Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 2nd edition, 1994.
[3] J. F. Hughes and J. O. Shallit. On the number of multiplicative partitions. American Mathematical Monthly, 90(7):468-471, 1983.
[4] Arnold Knopfmacher and ME Mays. A survey of factorization counting functions. International Journal of Number Theory, 1(04):563-581, 2005.
[5] Arnold Knopfmacher and ME Mays. Ordered and unordered factorizations of integers. Mathematica J., 10:72-89, 2006.
[6] P. A. Kennedy D. St. John M. J. Burke, P. E. Kehle. Number triangles, in navigating through number and operations in grades 9-12. National Council of Teachers of Mathematics, Reston VA 2006.
[7] NRich. Multiplication arithmagons, 2012.