Combinatorics

Compute binomial coefficients (combinations):

30 choose 18

Compute a Frobenius number:

Frobenius number {4, 7, 12}

Find the partitions of an integer:

integer partitions of 10

Graph Theory

Compute the properties of a named graph:

Pappus graph

Compare several graphs:

Petersen graph, icosahedral graph

Analyze a graph specified by adjacency rules:

1->2, 2->3, 3->1, 3->4, 4->1

Point Lattices

Compute the properties of a lattice:

face-centered cubic

Compute the properties of a root lattice:

A4 root lattice

Compare several lattices:

simple cubic, simple hexagonal

Sequences

Compute a possible formula and continuation for a sequence:

1, 4, 9, 16, 25, ...

Sum an incompletely specified infinite series:

1/2 + 1/4 + 1/8 + 1/16 + ...

Recurrences

Solve a recurrence:

g(n+1)=n^2+g(n)

Specify initial values:

f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2

Find a recurrence satisfied by a given sequence:

fibonacci(n) recurrence

Ackermann Function

Evaluate the Ackermann function:

ackermann[2,3]

what is ackermann 4,1?

ack(2,ack(2,1))