Median and mode conjecture for crosscap number and unoriented genus of prime alternating knots
Median and mode conjecture for crosscap number and unoriented genus of prime alternating knots
Let be the crossing number of a prime alternating knot. For each , consider the distributions of its crosscap number and unoriented genus among all -crossing prime alternating knots.
Median and mode conjecture. For any , the medians and modes for and among all -crossing prime alternating knots equal
This conjecture extrapolates a pattern observed in the tabulated data; its status is open, and no proof or disproof is supplied.
Sources & referencesView supporting material
Primary source
Isaias Bahena, Thomas Kindred and Jason Parsley, “Crosscap numbers of alternating links via state codes”, arXiv:2512.09887 (2025).
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