SUBSET
Combinatorial Routines
SUBSET,
a C 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.
These include the enumeration, generation, random
selection, ranking and unranking of

COMP, compositions of an integer;

COMPNZ, compositions of an integer with no zero parts;

EQUIV's, partitions of a set of N objects;

I4_PARTITION's, partitions of an integer;

I4POLY's, integer polynomials in factorial, Newton,
power sum, or Taylor form;

I4VEC's, integer vectors;

KSUB's, subsets of size K, from a set of N objects;

MULTIPERM's, permutations of the N objects, some of which
are indistinguishable.

PERM's, permutations of the first N integers;

R8POLY's, real polynomials in factorial, Newton,
power sum, or Taylor form;

subsets of a set of N objects;

vectors whose entries range from 1 to N;

YTB's, Young tables;
Other objects considered include

the Bell numbers,

Catalan numbers,

congruence equations.

continued fractions,

DEC's, decimal numbers represented as a mantissa and a power of 10;

DERANGE's, derangements (permutations that leave no element
in place),

DVEC's, decimal numbers represented as a vector of digits;

falling factorials (20*19*18...),

GRAY, Gray codes,

matrix permanents (similar to determinants, but harder to compute,
if you can believe that),

MorseThue numbers,

pentagonal numbers,

Pythagorean triples,

RAT's, rational numbers represented as a pair of integers;

rising factorials (7*8*9...).
Licensing:
The computer code and data files made available on this web page
are distributed under
the GNU LGPL license.
Languages:
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 C library which
carries out a backtrack search for a set of binary decisions, using
reverse communication.
CHANGE_MAKING,
a C library which
considers the change making problem,
in which a given sum is to be formed using coins of various denominations.
COMBO,
a C library which
contains many combinatorial routines.
KNAPSACK_01,
a C library which
uses brute force to solve small versions of the 0/1 knapsack problem;
LEGENDRE_PRODUCT_POLYNOMIAL,
a C library which
defines Legendre product polynomials, creating a multivariate
polynomial as the product of univariate Legendre polynomials.
MONOMIAL,
a C 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.
POLYNOMIAL,
a C library which
adds, multiplies, differentiates, evaluates and prints multivariate
polynomials in a space of M dimensions.
SET_THEORY,
a C library which
demonstrates various set theoretic operations
using several models of a set.
subset_test
TOMS515,
a C 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.
UBVEC,
a C library which
demonstrates how unsigned binary vectors, strings of 0's and 1's,
can represent nonnegative integers or subsets or other mathematical
objects, for which various arithmetic and logical operations can
be defined.
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Source Code:
Last revised on 11 August 2019.