How this calculation works
Count forests on labeled vertices split into two tree components of the requested sizes.
Choose the labels for one component, then multiply by the number of trees in each componentA worked example
For sizes 3 and 2, choose three labels in ten ways and build three trees on them.
Good to know
The components are unordered. Equal sizes introduce a factor of two.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count forests on labeled vertices split into two tree components of the requested sizes.
The primary result is labeled “Two-component forests”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The components are unordered. Equal sizes introduce a factor of two.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
For sizes 3 and 2, choose three labels in ten ways and build three trees on them.
Which rule does this calculator apply?
Choose the labels for one component, then multiply by the number of trees in each component