joriki's New Writeupshttp://everything2.com/?node=New%20Writeups%20Atom%20Feed&foruser=joriki2009-05-18T12:50:48Zlaminated lattice (thing)http://everything2.com/user/joriki/writeups/laminated+latticejorikihttp://everything2.com/user/joriki2009-05-18T12:50:48Z2009-05-18T12:50:48Z<p>Every (n+1)-dimensional <a href="/title/lattice">lattice</a> is built up of <a href="/title/layer">layer</a>s of n-dimensional lattices. An (n+1)-dimensional laminated lattice is built up of layers of n-dimensional laminated lattices packed as densely as possible. Thus, the definition of a laminated lattice is <a href="/title/recursive">recursive</a>, and what counts as a laminated lattice in n dimensions depends on what happens in all the lower dimensions. The process of "laminating" lattices can be viewed as a "greedy" way of constructing dense lattices. In some dimensions, this construction yields the densest possible lattices; in other dimensions, there are denser lattices that cannot be constructed in this way.</p>