partitions (version 1.10-9)

riffle: Riffle shuffles

Description

Enumeration of riffle shuffles

Usage

genrif(v)
riffle(p,q=p)

Value

Returns a matrix of class partition with columns being riffle shuffles

Arguments

p,q,v

In function riffle(), integers p,q specify the length of the two increasing sequences. In function genrif(), the elements of v specify the lengths of all the increasing sequences: there are sum(v) cards in the pack

Author

Robin K. S. Hankin

Details

A riffle shuffle is a permutation of integers \(1,2,\ldots,n\) containing one or two rising sequences.

A generalized riffle shuffle, or \(r\)-riffle shuffle, contains at most \(r\) rising sequences. This is not implemented in the package (earlier versions included a buggy version; the difficulty is ensuring that sequences do not appear more than once).

• riffle(p,q) returns all riffle shuffles with rising sequences of 1:p and (p+1):q

• genrif(v) returns all riffle shuffles with rising sequences having lengths the entries of v, the deck being numbered consecutively

See Also

parts

Examples

riffle(3,4)
genrif(1:3)