The z-Parity Alexander polynomial span conjecture for virtual knots

Let KK be a virtual knot. Let nn be the minimum number of real (non-virtual) crossings in any diagram of KK, and let zemaxz^{e_{\max}} and zeminz^{e_{\min}} be, respectively, the highest and lowest powers of zz appearing in the z-Parity Alexander Polynomial of KK.

z-Parity Alexander polynomial span conjecture. The exponents satisfy

emaxeminn.e_{\max}-e_{\min}\leq n.

The authors state that they verified this conjecture computationally for virtual knots with fewer than 66 real crossings. Its general status is not established in the supplied text.

Sources & referencesView supporting material

Primary source

Aaron Kaestner and Louis H. Kauffman, “Parity Biquandles”, arXiv:1103.2825 (2011).

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