# combo

combo, a Python code which ranks, unranks, enumerates, lists and randomly selects balanced sequences, cycles, graphs, Gray codes, subsets, partitions, permutations, restricted growth functions, Pruefer codes and trees.

The objects include:

• BAL, balanced sequences, included nested parentheses, Dyck lattice paths, ballot paths;
• CYCLE, permutations of the first N integers in cycle form;
• GRAPH, graphs stored as a list of edges.
• GRAY, Gray codes;
• KNAPSACK, optimally filling a knapsack of given size using a set of smaller objects;
• KSUBSET, subsets of size exactly K from a set of N objects;
• NPART, partitions of an integer having exactly N parts;
• PART, partitions of an integer;
• PERM, permutations of the first N integers in standard form;
• PRUEFER, Pruefer codes;
• RGF, restricted growth functions;
• SETPART, partitions of a set;
• SUBSET, subsets of a set of N objects;
• TABLEAU, tableaus;
• TREE, trees;

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.

### Languages:

combo is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

monomial, a Python code 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 Python code which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of m dimensions.

python_combinatorics, a Python code which considers a variety of problems in combinatorics involving counting, combinations, permutations, and so on.

subset, a Python code which generates, ranks and unranks various combinatorial objects.

unicycle, a Python code which considers permutations containing a single cycle, sometimes called cyclic permutations.

### Source Code:

Last revised on 28 September 2021. <%-- John Burkardt -->