Coordinate knots

Henrich, Allison; Kutty, Sriram; Tan, Grace

doi:10.2140/involve.2025.18.517

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Coordinate knots

Allison Henrich, Sriram Kutty and Grace Tan

Vol. 18 (2025), No. 3, 517–538

DOI: 10.2140/involve.2025.18.517

Abstract

Coordinate knots are knot-like objects represented by two-dimensional diagrams. As the name suggests, these diagrams are placed on the Cartesian plane; line segments of a coordinate knot are all placed on the integer gridlines. Coordinate knots are similar to rectangular arc-presentations as well as quantum mosaic knots, though they are constructed in a different way. Because they are a new representation of knots, there is still much to be asked and answered. This paper serves as a foundation for coordinate knot theory.

Keywords

knot, grid diagram, mosaic knots, integer lattice

Mathematical Subject Classification

Primary: 57K10

Milestones

Received: 13 September 2023

Revised: 11 December 2023

Accepted: 13 December 2023

Published: 28 April 2025

Communicated by Colin Adams

Authors

Allison Henrich
Mathematics Department Seattle University Seattle, WA United States

Sriram Kutty
University of Washington Seattle, WA United States

Grace Tan
Redmond High School Redmond, WA United States

Vol. 18, No. 3, 2025