A374944 a(n) is the maximum over the minimum crossing numbers of all Legendrian knots that can be realized on a Legendrian n-mosaic.

0, 0, 0, 0, 3, 8

Offset: 1

Author

Margaret Kipe, Samantha Pezzimenti, Leif Schaumann, Luc Ta, Wing Hong Tony Wong, Jul 24 2024

Keywords

• nonn
• hard
• more
• bref

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.

Examples

			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.
		

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.

Crossrefs

Cf. A374939, A374942, A374943, A374945, A374946, A374947.