Vol. 8, No. 3, 2015

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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

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 (p,p+1)-torus knots and some 3-bridge knots are given requiring one more stick than the lower bound guarantees.

lattice knots, stick number, composition, bridge number
Mathematical Subject Classification 2010
Primary: 57M50
Received: 21 October 2013
Revised: 21 May 2014
Accepted: 23 May 2014
Published: 5 June 2015

Communicated by Colin Adams
Ryan Bailey
The University of Texas at Austin
Department of Mathematics
1 University Station C1200
Austin, TX 78712
United States
Hans Chaumont
Department of Mathematics
University of Wisconsin–Madison
480 Lincoln Drive
Madison, WI 53706
United States
Melanie Dennis
Department of Mathematics
Dartmouth College
27 North Main Street
Hanover, NH 03755
United States
Jennifer McLoud-Mann
Division of Engineering and Mathematics
University of Washington Bothell
Box 358538
18115 Campus Way NE
Bothell, WA 98011
United States
Elise McMahon
Manteca, CA 95337
United States
Sara Melvin
Department of Mathematics
The University of Texas at Tyler
3900 University Boulevard
Tyler, TX 75799
United States
Geoffrey Schuette
Department of Mathematics
The University of Texas at Arlington
411 South Nedderman Drive
478 Pickard Hall
Arlington, TX 76019
United States