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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
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Abstract |
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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 -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
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Mathematical Subject Classification 2010
Primary: 57M50
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Milestones
Received: 21 October 2013
Revised: 21 May 2014
Accepted: 23 May 2014
Published: 5 June 2015
Communicated by Colin Adams
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Authors |
| Ryan Bailey | |
| The University of Texas at
Austin Department of Mathematics 1 University Station C1200 Austin, TX 78712 United States |
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| Hans Chaumont | |
| Department of Mathematics University of Wisconsin–Madison 480 Lincoln Drive Madison, WI 53706 United States |
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| Melanie Dennis | |
| Department of Mathematics Dartmouth College 27 North Main Street Hanover, NH 03755 United States |
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| Jennifer McLoud-Mann | |
| Division of Engineering and
Mathematics University of Washington Bothell Box 358538 18115 Campus Way NE Bothell, WA 98011 United States |
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| Elise McMahon | |
| Manteca, CA 95337 United States |
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| Sara Melvin | |
| Department of Mathematics The University of Texas at Tyler 3900 University Boulevard Tyler, TX 75799 United States |
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| Geoffrey Schuette | |
| Department of Mathematics The University of Texas at Arlington 411 South Nedderman Drive 478 Pickard Hall Arlington, TX 76019 United States |
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