3 results
WEIGHT ELEMENTS OF THE KNOT GROUPS OF SOME THREE-STRAND PRETZEL KNOTS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 2 / October 2018
- Published online by Cambridge University Press:
- 01 August 2018, pp. 305-318
- Print publication:
- October 2018
-
- Article
-
- You have access
- Export citation
Erratum: The Lehmer Polynomial and Pretzel Links
-
- Journal:
- Canadian Mathematical Bulletin / Volume 45 / Issue 2 / 01 June 2002
- Published online by Cambridge University Press:
- 20 November 2018, p. 231
- Print publication:
- 01 June 2002
-
- Article
-
- You have access
- Export citation
The Lehmer Polynomial and Pretzel Links
-
- Journal:
- Canadian Mathematical Bulletin / Volume 44 / Issue 4 / 01 December 2001
- Published online by Cambridge University Press:
- 20 November 2018, pp. 440-451
- Print publication:
- 01 December 2001
-
- Article
-
- You have access
- Export citation
-
In this paper we find a formula for the Alexander polynomial
${{\Delta }_{p1,...,{{p}_{k}}\left( x \right)}}$ of pretzel knots and links with 
$\left( {{p}_{1}},...,{{p}_{k}},-1 \right)$ twists, where 
$k$ is odd and 
${{p}_{1}},...,{{p}_{k}}$ are positive integers. The polynomial 
${{\Delta }_{2,3,7}}\left( x \right)$ is the well-known Lehmer polynomial, which is conjectured to have the smallest Mahler measure among all monic integer polynomials. We confirm that ${{\Delta }_{2,3,7}}\left( x \right)$ has the smallest Mahler measure among the polynomials arising as ${{\Delta }_{p1,...,{{p}_{k}}\left( x \right)}}$.
