Straight knots
Abstract
Jablan and Radović originally defined two invariants called the Meander number and OGC number of knots for certain classes of knots. We generalize these definitions to all knots and name the straight number and contained straight number of a knot, respectively, and prove they are well defined. We answer two questions and prove a generalization of a conjecture of Jablan and Radović. We also give some relations to crossing number and petal number. Then we compute the straight numbers for all the knots in the standard knot table and present some interesting questions and the complete table of knots with 10 or fewer crossing and their straight number and contained straight number.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 DOI:
 10.48550/arXiv.1801.10428
 arXiv:
 arXiv:1801.10428
 Bibcode:
 2018arXiv180110428O
 Keywords:

 Mathematics  Geometric Topology;
 57M25;
 57M27
 EPrint:
 16 page, 7 figures, 1 table. Questions and comments are welcome  Added reference to a paper that is related and answered questions they have asked. Made two corrections in the table