A374944 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=1..6.

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 = 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.

PROG

(Python, Rust) //See Margaret Kipe links

CROSSREFS

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

Sequence in context: A137125 A103319 A341812 * A153021 A155979 A120669

Adjacent sequences: A374941 A374942 A374943 * A374945 A374946 A374947

KEYWORD

nonn,hard,more,bref

AUTHOR

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

STATUS

approved