L-Tromino Tilings for Portions of Square Lattice

Overview

Domino tiling problem for (m, n)-grid was solved by Kasteleyn, Temperley and Fisher in 1961. L-tromino is a 2x2 rectangle without one cell. We consider the L-tromino tilings problem for (m,n)- grid when mn is not divisible by 3. We show that the alternative sums of the first row of the L-tromino tilings matrix vanish if mn = 2(mod 3), and similar relation holds for the second row of the L-tromino tiling matrix if mn = 1(mod 3). As an application of this result, we obtain that the number of L-tromino tilings for (m, 7)-grid without (2, 4)-cell is two times more than the similar number for (m, 7)-grid without (2, 3)-cell.

Awards (1)

• Mu Alpha Theta, National High School and Two-Year College Mathematics Honor Society: Second Award of $1,000 $1,000

Competition history

• ISEF 2023 Mathematics · Entry MATH042 · Dallas, Texas, United States

Resources

• ISEF abstract page ↗

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