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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 {\displaystyle n} items that can be obtained by a single riffle shuffle, in which a sorted deck of n {\displaystyle n} cards is cut into two packets and then the two packets are interleaved. Beginning with an ordered set , 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 {\displaystyle } -shuffle, for numbers p {\displaystyle p} and q {\displaystyle q} with p + q = n {\displaystyle p+q=n} , is a riffle in which the first packet has p {\displaystyle p} cards and the second packet has q {\displaystyle q} cards.