×

Answer to a question by Nakamura, Nakanishi, and Satoh involving crossing numbers of knots. (English) Zbl 1396.57021

Summary: In this paper we give a positive answer to a question raised by T. Nakamura, Y. Nakanishi and S. Satoh [Yokohama Math. J. 59, 91–97 (2013; Zbl 1298.57005)] concerning an inequality involving crossing numbers of knots. We show it is an equality only for the trefoil and for the figure-eight knots.

MSC:

57M27 Invariants of knots and \(3\)-manifolds (MSC2010)

Citations:

Zbl 1298.57005
PDFBibTeX XMLCite
Full Text: Euclid

References:

[1] R.H. Fox: A quick trip through knot theory; in Topology of 3-manifolds and related topics, ed. by M. K. Fort, Prentice-Hall, N. J., 1962. · Zbl 1246.57002
[2] F. Harary and L.H. Kauffman: Knots and graphs. I. Arc graphs and colorings, Adv. in Appl. Math. 22 (1999), 312-337. · Zbl 1128.57301 · doi:10.1006/aama.1998.0634
[3] P. Lopes and J. Matias: Minimum number of Fox colors for small primes, J. Knot Theory Ramifications 21 (2012), 1250025, 1-12. · Zbl 1241.57019 · doi:10.1142/S0218216511009728
[4] T. Nakamura, Y. Nakanishi and S. Satoh: The pallet graph of a Fox coloring, Yokohama Math. J. 59 (2013), 91-97. · Zbl 1298.57005
[5] A. Stoimenow: Maximal determinant knots, Tokyo J. Math. 30 (2007), 73-97. · Zbl 1131.57011 · doi:10.3836/tjm/1184963648
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.