enumeration problem
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Examples forCombinatorics

Factorials & Combinations

Do computations with factorials:

100!
12! / (4! * 6! * 2!)

Compute binomial coefficients (combinations):

30 choose 18

Compute a multinomial coefficient:

multinomial(3,4,5,8)

Evaluate a double factorial binomial coefficient:

DFBC(12, 6)
DFBC(n, n-1)
Permutations »

Compute the permutations of a set:

permutations of {a, b, c, d}

Count permutations:

number of permutations of 23 elements

Do algebra with permutations:

perm (1 2 3 4)^3(1 2 3)^-1

Integer Partitions

Compute the partitions of an integer:

integer partitions of 10

Specify a constraint on the number of parts:

partitions of 38 into 6 parts
odd partitions of 14

Restrict to partitions into distinct parts:

partition 84 into distinct parts

Compute the number of partitions:

number of partitions of 1250

Integer Compositions

Compute the compositions of an integer:

compositions of 33

Specify a constraint on the parts:

compositions of 12 into even parts

Enumeration Problems

Count the number of possible colored bracelets:

bracelets 7 beads, 4 colors

Count the number of possible fixed necklaces:

fixed necklaces with 6 beads and 3 colors

Count Lyndon words:

5-ary Lyndon words of length 12

Combinatorial Functions

Compute a Bernoulli number:

Bernoulli B(16)

Compute a Stirling number:

S1(8, 4)

Compute a Frobenius number:

Frobenius number {4, 7, 12}

Compute Catalan numbers:

Catalan number

Compute Clebsch–Gordan coefficients:

Clebsch-Gordan calculator

Compute Wigner coefficients:

wigner 3j
wigner 6j

Latin Squares

Get information about Latin squares:

Latin squares

Compute the number of Latin squares of a specified size:

6x6 Latin squares

Count normalized Latin squares:

normalized Latin squares of order 5

Compute bounds on the number of large-size Latin squares:

size 89 Latin square

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