On Upper Bounds for Toroidal Mosaic Numbers

Michael J. Carlisle; Michael S. Laufer

doi:10.1007/s11128-013-0576-y

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arXiv · 1206.4227

On Upper Bounds for Toroidal Mosaic Numbers

Michael J. Carlisle·Michael S. Laufer

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Abstract

In this paper, we work to construct mosaic representations of knots on the torus, rather than in the plane. This consists of a particular choice of the ambient group, as well as different definitions of contiguous and suitably connected. We present conditions under which mosaic numbers might decrease by this projection, and present a tool to measure this reduction. We show that the order of edge identification in construction of the torus sometimes yields different resultant knots from a given mosaic when reversed. Additionally, in the Appendix we give the catalog of all 2 by 2 torus mosaics.

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BibTeX RIS

Michael J. Carlisle, Michael S. Laufer. 2013-04-08. On Upper Bounds for Toroidal Mosaic Numbers. https://doi.org/10.1007/s11128-013-0576-y

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