Combinatorics
Factorials and 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)
compute 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 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 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