Vol. 8, No. 3, 2015

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors’ Interests Scientific Advantages Submission Guidelines Submission Form Ethics Statement Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print)
Stick numbers in the simple hexagonal lattice

Ryan Bailey, Hans Chaumont, Melanie Dennis, Jennifer McLoud-Mann, Elise McMahon, Sara Melvin and Geoffrey Schuette

Vol. 8 (2015), No. 3, 503–512
Abstract

In the simple hexagonal lattice, bridge number is used to establish a lower bound on stick numbers of knots. This result aids in giving a new proof that the minimal stick number is 11. In addition, the authors establish upper bounds for the stick number of a composite knot. Constructions for $\left(p,p+1\right)$-torus knots and some 3-bridge knots are given requiring one more stick than the lower bound guarantees.

Keywords
lattice knots, stick number, composition, bridge number
Primary: 57M50