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A374944
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a(n) is the maximum over the minimum crossing numbers of all Legendrian knots that can be realized on a Legendrian n-mosaic.
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7
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OFFSET
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1,5
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COMMENTS
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A Legendrian n-mosaic is an n X n array of the 10 tiles given in Figure 5 of Pezzimenti and Pandey. These tiles represent part of a Legendrian curve in the front projection.
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LINKS
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EXAMPLE
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For n = 5, the only Legendrian knots that can be realized on a Legendrian 5-mosaic are positive and negative Legendrian trefoils, which have a minimal crossing number of 3, and Legendrian unknots, which have a minimal crossing number of 0. Therefore, a(5) = 3.
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PROG
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(Python, Rust) //See Margaret Kipe links
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CROSSREFS
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KEYWORD
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nonn,hard,more,bref,new
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AUTHOR
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STATUS
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approved
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