Combinatorial Routines

SUBSET, a MATLAB library which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems. Some routines for continued fractions are included.

Combinatorial operations include the enumeration, generation, random selection, ranking and unranking of

Other objects considered include


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


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

Related Data and Programs:

BACKTRACK_BINARY_RC, a MATLAB library which carries out a backtrack search for a set of binary decisions, using reverse communication.

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

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

COMBO, a MATLAB library which contains many combinatorial routines.

GRAY_CODE_DISPLAY, a MATLAB program which computes the Hamming distance tables for both the binary and Gray codes, and displays 3D plots that illustrate how the Gray code does a better job of providing nearby representations for nearby numbers.

MONOMIAL, a MATLAB 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.

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

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

SET_THEORY, a MATLAB library which demonstrates MATLAB commands that implement various set theoretic operations.


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

TOMS515, a MATLAB library which can select subsets of size K from a set of size N. This is a version of ACM TOMS Algorithm 515, by Bill Buckles, Matthew Lybanon.

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

Source Code:

Last revised on 23 March 2019.