# multicool: Permutations of Multisets in Cool-Lex Order

A set of tools to permute multisets without loops or hash tables and to generate integer partitions. The permutation functions are based on C code from Aaron Williams. Cool-lex order is similar to colexicographical order. The algorithm is described in Williams, A. Loopless Generation of Multiset Permutations by Prefix Shifts. SODA 2009, Symposium on Discrete Algorithms, New York, United States. The permutation code is distributed without restrictions. The code for stable and efficient computation of multinomial coefficients comes from Dave Barber. The code can be download from http://home.comcast.net/~tamivox/dave/multinomial/index.html and is distributed without conditions. The package also generates the integer partitions of a positive, non-zero integer n. The C++ code for this is based on Python code from Jerome Kelleher which can be found here http://jeromekelleher.net/partitions.php. The C++ code and Python code are distributed without conditions.

- Author
- James Curran, Aaron Williams, Jerome Kelleher, Dave Barber
- Date of publication
- 2015-10-28 18:39:18
- Maintainer
- James Curran <j.curran@auckland.ac.nz>
- License
- GPL-2
- Version
- 0.1-9

## Man pages

- allPerm
- Generate and return all permutations of a multiset
- allPerm
- Generate and return all permutations of a multiset
- Bell
- Compute the Bell numbers
- Bell
- Compute the Bell numbers
- genComp
- Generate all, or a subset, of the integer partitions of an...
- genComp
- Generate all, or a subset, of the integer partitions of an...
- initMC
- Initialise the permutation object
- initMC
- Initialise the permutation object
- multinom
- Calculate multinomial coefficients
- multinom
- Calculate multinomial coefficients
- nextPerm
- Return the next permutation of the multiset
- nextPerm
- Return the next permutation of the multiset
- Stirling2
- Compute Stirling numbers of the second kind
- Stirling2
- Compute Stirling numbers of the second kind

## Files in this package

multicool |

multicool/src |

multicool/src/multicool.cpp |

multicool/src/multinomial.h |

multicool/src/compositions.cpp |

multicool/src/RcppExports.cpp |

multicool/NAMESPACE |

multicool/R |

multicool/R/genComp.R |

multicool/R/nextPerm.R |

multicool/R/multinom.R |

multicool/R/Stirling2.R |

multicool/R/initMC.r |

multicool/R/RcppExports.R |

multicool/R/allPerm.R |

multicool/R/zzz.R |

multicool/README.md |

multicool/MD5 |

multicool/DESCRIPTION |

multicool/man |

multicool/man/Bell.Rd |

multicool/man/initMC.Rd |

multicool/man/multinom.Rd |

multicool/man/allPerm.Rd |

multicool/man/Stirling2.Rd |

multicool/man/genComp.Rd |

multicool/man/nextPerm.Rd |