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 items that can be obtained by a single riffle shuffle, in which a sorted deck of 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.[1] The permutations with 1 rising sequence are the identity permutations.
As a special case of this, a -shuffle, for numbers and with , is a riffle in which the first packet has cards and the second packet has cards.[2]
^Aldous, David; Diaconis, Persi (1986), "Shuffling cards and stopping times" (PDF), The American Mathematical Monthly, 93 (5): 333–348, doi:10.2307/2323590, JSTOR 2323590, MR 0841111
^Weibel, Charles (1994). An Introduction to Homological Algebra, p. 181. Cambridge University Press, Cambridge.
and 11 Related for: Riffle shuffle permutation information
the mathematics of permutations and the study of shuffling playing cards, a riffleshufflepermutation is one of the permutations of a set of n {\displaystyle...
during the shuffle. There are two types of perfect riffleshuffles: if the top card moves to be second from the top then it is an in shuffle, otherwise...
ways of interlacing them. The interlacing is given by the riffleshufflepermutation. The shuffle algebra on a finite set is the graded dual of the universal...
by this type of shuffle, and a Gilbreath permutation is a permutation that can be formed by a Gilbreath shuffle. A Gilbreath shuffle consists of the following...
involutions are enumerated by Motzkin numbers. Riffleshufflepermutation, a subclass of the vexillary permutations Guibert, O.; Pergola, E.; Pinzani, R. (2001)...
likely it is that a riffle results in a particular riffleshufflepermutation, it takes 5 riffles before the total variation distance of a 52-card deck...
resolution versions can be obtained at PermPal Baxter permutation Riffleshufflepermutation Albert, Michael H.; Elder, Murray; Rechnitzer, Andrew; Westcott...
Gilbert–Shannon–Reeds model for probability distribution of riffleshufflepermutations in shuffling playing cards reported. Peter Hilton starts work with Beno...
the elements x k {\displaystyle x_{k}} is preserved in the riffleshuffle: the riffleshuffle merely splits the ordered sequence into two ordered sequences...
model of random shuffles, one can show that the number of times one needs to shuffle an n-card deck of cards, using riffleshuffles, to get a distribution...
distribution on permutations of a set of n items that, according to experiments by Persi Diaconis, accurately models human-generated riffleshuffles. In this...