Brunnian Clothes on the Runway: Not for the Bashful

Abstract

Yes, it is risque, said Laurent, but the purpose of fashion is to challenge, to flaunt unconventionality, to confront us with the evanescence of material goods. Vogue managing editor Danielle Witherspoon explained. clothes are made of a fabric with a rather unusual property. It is woven out of many, many tiny individually unknotted loops. It works just fine and has a wonderful drape. But the moment any one loop is broken, the entire piece of clothing falls apart into thousands of unlinked trivial loops lying at your feet. It's the hottest thing since Saran Wrap ponchos. Fashion aficionados were caught off guard, not ever having heard of Brunnian clothing before. Carol Pantaloon, a representative of Laurent Industries provided the details. You see, a link is just a set of closed loops that can be individually knotted and tangled together. Each loop is called a component. Figure 2 shows a random link of three components. very simplest link of n components is just a set of unknotted untangled rings, called the unlink of n components. Figure 3 displays the unlink of five components. We call a link Brunnian if the disappearance of any single component leaves an unlink of n 1 components. This has to hold no matter which component is removed. The simplest such link is the famous Borromean rings in Figure 4, named for the Borromeo family of the Italian Renaissance, who used it on their family crest.