A Full-Featured Open-Source Framework for Image Processing

Reptorian's Combinatorics Library

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Description

A library for permutation and combinatorial enumeration.

The library provides commands for generation, ranking (list2index),
and unranking (index2list) of many combinatorial structures.

Supported structures include permutations, combinations,
cartesian product, sum-constrained permutations,
incremental combination, and repeated distinct element (RDE)
variants of many of these structures.

RDE structures represent multisets where each element type
has a fixed number of occurrences.

The library is designed to enable deterministic traversal
and indexing of large combinatorial spaces inside G'MIC pipeline.

Enumeration Order and Indexing

All combinatorial structures in this library are:

Enumerated in lexicographic order (left-to-right comparison of elements)
Zero-based indexed (indices start at 0)

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Terminology

Permutations
Ordered arrangements of elements where position matters.

Combinations
Selections of elements where order does not matter.

Cartesian Product
The set of all ordered items formed by combining elements
from multiple sets.

Sum-constrained Combinatorics
Combinatorics tools for non-negative integers where the values
are restricted by a maximum sum constraint.

Incremental Combinations
Combinations represented as non-decreasing integer sequences.

Repeated Distinct Elements (RDE)
Combinatorial structures formed from multisets where each
element type has a fixed number of allowed occurrences.

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Commands

Permutations:

rep_permutations	rep_permutation_index2list	rep_permutation_list2index
rep_npr_permutations	rep_npr_permutation_index2list	rep_npr_permutation_list2index
rep_r_permutations	rep_r_permutation_index2list	rep_r_permutation_list2index

Combinations:

rep_ncr_combinations	rep_ncr_combination_index2list	rep_ncr_combination_list2index
rep_r_combinations	rep_r_combination_index2list	rep_r_combination_list2index

Cartesian Product:

rep_cartesian_product

rep_cartesian_product_index2list

rep_cartesian_product_list2index

Sum-Constrained Combinatorics:

rep_sum_permutations	rep_sum_permutation_index2list	rep_sum_permutation_list2index
rep_total_sum_permutations	rep_total_sum_permutation_index2list	rep_total_sum_permutation_list2index
rep_sum_combinations	rep_sum_combination_index2list	rep_sum_combination_list2index
rep_total_sum_combinations	rep_total_sum_combination_index2list	rep_total_sum_combination_list2index

Repeated Distinct Elements (RDE):

rep_rde_permutations	rep_rde_permutation_index2list	rep_rde_permutation_list2index
rep_rde_npr_permutations	rep_rde_npr_permutation_index2list	rep_rde_npr_permutation_list2index
rep_rde_combinations	rep_rde_combination_index2list	rep_rde_combination_list2index
rep_rde_compsel_perm	rep_rde_compsel_perm_index2list	rep_rde_compsel_perm_list2index
rep_rde_compsel_comb	rep_rde_compsel_comb_index2list	rep_rde_compsel_comb_list2index

Incremental Combinations:

rep_inc_combinations

rep_inc_combination_index2list

rep_inc_combination_list2index

G'MIC is an open-source software distributed under the CeCILL free software licenses (LGPL-like and/or
GPL-compatible). Copyrights (C) Since July 2008, David Tschumperlé - GREYC UMR CNRS 6072, Image Team.