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Open Quantum Systems Decoherence
Quantum Simulation
Entanglement Theory Quantum Correlations
On Upper Bounds for Toroidal Mosaic Numbers
arXiv
Authors: Michael J. Carlisle, Michael S. Laufer
Year
2012
Paper ID
8545
Status
Preprint
Abstract Read
~2 min
Abstract Words
96
Citations
N/A
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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- In this paper, we work to construct mosaic representations of knots on the torus, rather than in the plane.
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