'''Permutations''' ** http://www.cut-the-knot.org/do_you_know/permutation.shtml * ''Being able to count elements in the set V means the set can be written as {v1, v2, ..., vn}. However, a set may be counted in many different ways.'' * Various ways to define a permutation ** http://www.cut-the-knot.org/do_you_know/Perm.shtml *''There are many ways one can define a permutation, none of which is simple.'' '''Arrays''' * An analysis of permutations in arrays ** http://hal.archives-ouvertes.fr/docs/00/45/65/58/PDF/main.pdf * ''In order to analyze this kind of properties, we define an abstract interpretation working on multisets of values, and able to discover invariant equations about such multisets.'' * Question and Answers ** http://www.velocityreviews.com/forums/t131940-permutations-of-instances-in-array.html ---- '''Trees''' * Permutations as Trees ** http://www.luschny.de/math/factorial/combi/PermutationTrees.html * ''A permutation tree is a labeled rooted tree that has vertex set {0,1,2,..,n} and root 0, and in which each child is larger than its parent and the children are in ascending order from the left to the right. The power of a permutation tree is the number of descendants of the root. The height of a permutation tree is the number of descendants of the root on the longest chain starting at the root and ending at a leaf. The width of a permutation tree is the number of leafs.'' * ''The correspondence with the permutation is given by traversing the periphery of the tree starting at the right hand side of the root and recording a node whenever the node's right edge is passed.'' ---- See also MatroidTheory Project WikiBatics GoogleThis