|
Riffle Shuffle Permutation
In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of n items that can be obtained by a single riffle shuffle, in which a sorted deck of n cards is cut into two packets and then the two packets are interleaved (e.g. by moving cards one at a time from the bottom of one or the other of the packets to the top of the sorted deck). Beginning with an ordered set (1 rising sequence), mathematically a riffle shuffle is defined as a permutation on this set containing 1 or 2 rising sequences. The permutations with 1 rising sequence are the identity permutations. As a special case of this, a (p,q)-shuffle, for numbers p and q with p+q=n, is a riffle in which the first packet has p cards and the second packet has q cards.Weibel, Charles (1994). ''An Introduction to Homological Algebra'', p. 181. Cambridge University Press, Cambridge. Combinatorial enumeration Since a (p,q)-shuffle is completely determined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vexillary Permutation
In mathematics, a vexillary permutation is a permutation ''μ'' of the positive integers containing no subpermutation isomorphic to the permutation (2143); in other words, there do not exist four numbers ''i'' < ''j'' < ''k'' < ''l'' with ''μ''(''j'') < ''μ''(''i'') < ''μ''(''l'') < ''μ''(''k''). They were introduced by . The word "vexillary" means flag-like, and comes from the fact that vexillary permutations are related to of . showed that vexillary involutions are enumerated by |
