Editing Pretzel link (section)

==Some basic results==

The <math>(p_1,p_2,\dots,p_n)</math> pretzel link is a [[knot (mathematics)|knot]] [[iff]] both <math>n</math> and all the <math>p_i</math> are [[Even and odd numbers|odd]] or exactly one of the <math>p_i</math> is even.<ref name="kawauchi">Kawauchi, Akio (1996). ''A survey of knot theory''.  Birkhäuser. {{ISBN|3-7643-5124-1}}</ref>

The <math>(p_1,\,p_2,\dots,\,p_n)</math> pretzel link is [[Split link|split]] if at least two of the <math>p_i</math> are [[0 (number)|zero]]; but the [[Converse (logic)|converse]] is false.

The <math>(-p_1,-p_2,\dots,-p_n)</math> pretzel link is the [[mirror image]] of the <math>(p_1,\,p_2,\dots,\,p_n)</math> pretzel link.

The <math>(p_1,\,p_2,\dots,\,p_n)</math> pretzel link is isotopic to the <math>(p_2,\,p_3,\dots,\,p_n,\,p_1)</math> pretzel link. Thus, too, the <math>(p_1,\,p_2,\dots,\,p_n)</math> pretzel link is isotopic to the <math>(p_k,\,p_{k+1},\dots,\,p_n,\,p_1,\,p_2,\dots,\,p_{k-1})</math> pretzel link.<ref name="kawauchi" />

The <math>(p_1,\,p_2,\,\dots,\,p_n)</math> pretzel link is isotopic to the <math>(p_n,\,p_{n-1},\dots,\,p_2,\,p_1)</math> pretzel link. However, if one orients the links in a canonical way, then these two links have opposite orientations.