Representing Partitions with Tilings and Truncating the Partition Recurrence Formula
TITLE: Representing Partitions with Tilings and Truncating the Partition Recurrence Formula
A familiar pattern emerges from the number of ways to tile a 1xN rectangle using 1x1 squares and 1x2 dominos. These tilings can also be used to represent partitions of the number N. We can use these representatives to see exactly how the partition recurrence formula is counting the number of partitions of N. Truncating after the first two terms gives p(N)=p(N-1)+p(N-2) which is an overestimate of the actual number of partitions of N for N>4. By looking at just the partitions of N, it can be determined how far off the formula is by truncating after any term in the formula.