Kuriya, Takahito; Shehab, Omar The Lomonaco-Kauffman conjecture. (English) Zbl 1287.57012 J. Knot Theory Ramifications 23, No. 1, Article ID 1450003, 20 p. (2014). Summary: Samuel J. Lomonaco and Louis H. Kauffman [in: Lomonaco, Samuel J. jun. (ed.), Quantum information science and its contributions to mathematics. American Mathematical Society short course, January 3–4, 2009, Washington, DC, USA. Providence, RI: American Mathematical Society (AMS). Proceedings of Symposia in Applied Mathematics 68, 177–208 (2010; Zbl 1214.81055)] conjectured that tame knot theory and knot mosaic theory are equivalent. We give a proof of the Lomonaco-Kauffman conjecture. Cited in 1 ReviewCited in 11 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57M27 Invariants of knots and \(3\)-manifolds (MSC2010) 81P68 Quantum computation Keywords:knot mosaic; quantum knot; discrete structures for quantum computation; grid diagram Citations:Zbl 1214.81055 PDFBibTeX XMLCite \textit{T. Kuriya} and \textit{O. Shehab}, J. Knot Theory Ramifications 23, No. 1, Article ID 1450003, 20 p. (2014; Zbl 1287.57012) Full Text: DOI arXiv References: [1] DOI: 10.4064/fm190-0-3 · Zbl 1132.57006 · doi:10.4064/fm190-0-3 [2] DOI: 10.1007/s11128-008-0076-7 · Zbl 1144.81013 · doi:10.1007/s11128-008-0076-7 [3] DOI: 10.2140/gt.2008.12.941 · Zbl 1144.57012 · doi:10.2140/gt.2008.12.941 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.