Counting Divisions of a 2 × n Rectangular Grid
Jacob Brown · College Mathematics Journal · 2023
SummaryWhat is the number of ways to divide a 2×n rectangular grid, cutting along the grid lines, into k pieces? Are there formulas that calculate these number of divisions? If so, what do they look like? We show that all division-counting formulas will be polynomials on n for all k, and that for a fixed k, the division-counting polynomial will have degree 2k−2. We find these polynomials up to k=5.