An infinite family of Legendrian torus knots distinguished by cube number

For a knot K the cube number is a knot invariant defined to be the smallest it for which there is a cube diagram of size n for K. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number. (C) 2011 Elsevier B.V. All rights reserved.