## Combinatorics

Explore combinatorial possibilities and arrangements efficiently.

Combinatorics functions are vital for solving problems related to counting, arrangement, and combination. Calcul.io provides functions for permutations, combinations, factorials, and binomial coefficients. These functions are fundamental in fields like cryptography, computer science, and operations research.

Our combinatorics functions help you explore the vast possibilities within finite sets, enabling you to analyze complex scenarios and optimize solutions. Whether you are designing algorithms, studying graph theory, or solving puzzles, Calcul.io offers the combinatorial tools you need to achieve precise and insightful results.

bellNumbers | The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0. |

catalan | The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0. |

composition | The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n. |

stirlingS2 | he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1. |