Almost Alternating Link

Call a projection of a Link an almost alternating projection if one crossing change in the projection makes it analternating projection. Then an almost alternating link is a Link with an almost alternating projection, but noalternating projection. Every Alternating Knot has an almost alternating projection. A Prime Knot which isalmost alternating is either a Torus Knot or a Hyperbolic Knot. Therefore, no Satellite Knot is analmost alternating knot.

All nonalternating 9-crossing Prime Knots are almost alternating. Of the 393 nonalternating knots andlinks with 11 or fewer crossings, all but five are known to be almost alternating (3 of these have 11 crossings). The fate ofthe remaining five is not known. The , , and -Torus Knots are almost alternating.

References

Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 139-146, 1994.

• Parzen Apodization Function
• Pascal Distribution
• Pascal Line
• Pascal's Formula
• Pascal's Hexagrammum Mysticum
• Pascal's Limaçon
• Pascal's Rule
• Pascal's Theorem
• Pascal's Triangle
• Pascal's Wager
• Pasch's Axiom
• Pasch's Theorem
• Pass Equivalent
• Pass Move
• Patch
• Path
• Path Graph
• Path Integral
• Pathwise-Connected
• Patriarchal Cross
• Pauli Matrices
• Pauli Spin Matrices
• Payoff Matrix
• P-Circle
• Peacock's Tail