Kreher and Stinson Combinatorial Routines

COMBO is a FORTRAN77 library which includes routines for ranking, unranking, enumerating and randomly selecting balanced sequences, cycles, graphs, Gray codes, subsets, partitions, permutations, restricted growth functions, Pruefer codes and trees.

Routines are available to count, list, rank and unrank such objects

Some of these sets of objects can be ordered in several different ways, and in some cases, a separate set of ranking, unranking, and successor routines are available for the various orderings (lexical, colexical, revolving door, Trotter-Johnson).

Kreher and Stinson provide C source-code for the routines, as well as other information, at their web site.


The computer code and data files made available on this web page are distributed under the GNU LGPL license.


COMBO is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CHANGE_MAKING, a FORTRAN77 library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.

COMBINATION_LOCK, a FORTRAN77 program which simulates the process of determining the secret combination of a lock.

FLOYD, a FORTRAN77 library which implements Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.

KNAPSACK, a FORTRAN77 library which solves a variety of knapsack problems.

KNAPSACK_01, a FORTRAN77 library which uses brute force to solve small versions of the 0/1 knapsack problem;

KNAPSACK_01, a dataset directory which contains test data for the 0/1 knapsack problem;

LAMP, a FORTRAN77 library which solves linear assignment and matching problems.

LEGENDRE_PRODUCT_POLYNOMIAL, a FORTRAN77 library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

MONOMIAL, a FORTRAN77 library which enumerates, lists, ranks, unranks and randomizes multivariate monomials in a space of M dimensions, with total degree less than N, equal to N, or lying within a given range.

PARTIAL_DIGEST, a FORTRAN90 library which solves the partial digest problem.

PARTITION_PROBLEM, a FORTRAN77 library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

POLYNOMIAL, a FORTRAN77 library which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.

SELECT, a FORTRAN77 library which generates various combinatorial objects.

SET_THEORY, a FORTRAN90 library which demonstrates various set theoretic operations using several models of a set.

SUBSET, a FORTRAN77 library which generates, ranks and unranks various combinatorial objects.

SUBSET_SUM, a FORTRAN77 library which seeks solutions of the subset sum problem.

UNICYCLE, a FORTRAN77 library which considers permutations containing a single cycle, sometimes called cyclic permutations.


  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Second Edition,
    Springer, 1987,
    ISBN: 0387964673,
    LC: QA76.9.C65.B73.
  3. William Cody, Kenneth Hillstrom,
    Chebyshev Approximations for the Natural Logarithm of the Gamma Function, Mathematics of Computation,
    Volume 21, Number 98, April 1967, pages 198-203.
  4. Robert Fenichel,
    Algorithm 329: Distribution of Indistinguishable Objects into Distinguishable Slots,
    Communications of the ACM,
    Volume 11, Number 6, June 1968, page 430.
  5. Bennett Fox,
    Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, December 1986, pages 362-376.
  6. John Hart, Ward Cheney, Charles Lawson, Hans Maehly, Charles Mesztenyi, John Rice, Henry Thacher, Christoph Witzgall,
    Computer Approximations,
    Wiley, 1968,
    LC: QA297.C64.
  7. Brian Hayes,
    The Easiest Hard Problem,
    American Scientist,
    Volume 90, Number 2, March-April 2002, pages 113-117.
  8. Donald Kreher, Douglas Simpson,
    Combinatorial Algorithms,
    CRC Press, 1998,
    ISBN: 0-8493-3988-X,
    LC: QA164.K73.
  9. Pierre LEcuyer,
    Random Number Generation,
    in Handbook of Simulation,
    edited by Jerry Banks,
    Wiley, 1998,
    ISBN: 0471134031,
    LC: T57.62.H37.
  10. Peter Lewis, Allen Goodman, James Miller,
    A Pseudo-Random Number Generator for the System/360,
    IBM Systems Journal,
    Volume 8, 1969, pages 136-143.
  11. Albert Nijenhuis, Herbert Wilf,
    Combinatorial Algorithms for Computers and Calculators,
    Second Edition,
    Academic Press, 1978,
    ISBN: 0-12-519260-6,
    LC: QA164.N54.
  12. Robert Sedgewick,
    Algorithms in C,
    Addison-Wesley, 1990,
    ISBN: 0-201-51425-7,
    LC: QA76.73.C15S43.
  13. Jack vanLint, Richard Wilson,
    A Course in Combinatorics,
    Cambridge, 1992,
    ISBN: 0-521-42260-4,
    LC: QA164.L56.
  14. ML Wolfson, HV Wright,
    Algorithm 160: Combinatorial of M Things Taken N at a Time,
    Communications of the ACM,
    Volume 6, Number 4, April 1963, page 161.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 22 August 2012.