The Combinatorics of Occam's Razor

Understand

Occam's Razor tells us to pick the simplest model that fits our observations.

• In order to make sense of his process mathematically, we interpret it in the context of posets of functions.
• Our approach leads to some unusual new combinatorial problems concerning functions between finite sets.
• The same ideas are used to define a nicely behaved and apparently unknown analogue of the rank of a group.