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Wrong answer for certain connect sum diagrams #18

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NathanDunfield opened this issue Dec 26, 2022 · 0 comments
Open

Wrong answer for certain connect sum diagrams #18

NathanDunfield opened this issue Dec 26, 2022 · 0 comments

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@NathanDunfield
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Here is a 9-crossing alternating diagram with is the connect sum of two trefoils:

>>> pd = [(6, 15, 7, 16), (16, 6, 17, 5), (10, 13, 11, 14), (12, 9, 13, 10), 
...       (8, 11, 9, 12),  (14, 7, 15, 8), (2, 18, 3, 17), (18, 4, 1, 3), 
...       (4, 2, 5, 1)]
>>> knot_floer_homology.pd_to_hfk(pd)['total_rank']
30

Now, the total rank of HFK is odd for any knot, and in this case is 9. We do get the right answer from this 7 crossing diagram:

>>> pd = [(10,14,11,13),(14,12,1,11),(2,9,3,10),(4,7,5,8),(8,5,9,6),(6,3,7,4),(12,2,13,1)]
>>> knot_floer_homology.pd_to_hfk(pd)['total_rank']
9

Now the original ComputeHFK rejects both of the above diagrams with the message Incorrect Planar Diagram. That knot_floer_homology accepts these diagrams is presumably due to #12 which fixed #10 by allowing a crossing to be attached by the last strand in GetSmallGirthMorseCode.

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