OFFSET

1,5

COMMENTS

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.

Two knots have the same smooth knot type if and only if they are related by an ambient isotopy.

LINKS

Margaret Kipe, Python

Margaret Kipe, Rust

S. Pezzimenti and A. Pandey, Geography of Legendrian knot mosaics, Journal of Knot Theory and its Ramifications, 31 (2022), article no. 2250002, 1-22.

EXAMPLE

For n = 2, there is only a(2) = 1 smooth knot family with Legendrian representatives realizable on a Legendrian 2-mosaic, namely unknots.

For n = 5, every Legendrian 5-mosaic depicts either an unknot or a trefoil. Since unknots and trefoils are not ambient-isotopic, we have a(5) = 2.

PROG

(Python, Rust) //See Margaret Kipe links

CROSSREFS

KEYWORD

hard,more,nonn

AUTHOR

STATUS

approved