The Tilings of Deficient Squares by Ribbon *L*-Tetrominoes Are Diagonally Cracked

Show more

References

[1] Chao, M., Levenstein, D., Nitica, V. and Sharp, R. (2013) A Coloring Invariant for Ribbon L-Tetrominoes. Discrete Mathematics, 313, 611-621.

https://doi.org/10.1016/j.disc.2012.12.007

[2] Nitica, V. (2003) Rep-Tiles Revisited, in the Volume MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics. American Mathematical Society.

[3] Kasteleyn, P.M. (1961) The Statistics of Dimers on a Lattice. Physica, 27, 1209-1225.

https://doi.org/10.1016/0031-8914(61)90063-5

[4] Nitica, V. (2004-2005) Tiling a Deficient Rectangle by L-Tetrominoes. Journal of Recreational Mathematics, 33, 259-271.

[5] Golomb, S.W. (1994) Polyominoes, Puzzles, Patterns, Problems, and Packings. 2nd Edition, Princeton University Press.

[6] Hochberg, R. (2015) The Gap Number of the T-Tetromino. Discrete Mathematics, 338, 130-138.

https://doi.org/10.1016/j.disc.2014.09.001

[7] Zhan, S. (2012) Tiling a Deficient Rectangle with t-Tetrominoes.

https://www.math.psu.edu/mass/reu/2012/report/Tiling Deficient Rectangles with T-Tetrominoes.pdf

[8] Junius, P. and Nitica, V. (2017) Tiling Rectangles with Gaps by Ribbon Right Trominoes. Open Journal of Discrete Mathematics, 7, 87-102.

https://doi.org/10.4236/ojdm.2017.72010

[9] Nitica, V. (2015) Every Tiling of the First Quadrant by Ribbon L n-Ominoes Follows the Rectangular Pattern. Open Journal of Discrete Mathematics, 5, 11-25.

https://doi.org/10.4236/ojdm.2015.52002

[10] Calderon, A., Fairchild, S., Nitica, V. and Simon, S. (2016) Tilings of Quadrants by L-Ominoes and Notched Rectangles. Topics in Recreational Mathematics, 7, 39-75.

[11] Nitica, V. (2016) On Tilings of Quadrants and Rectangles and Rectangular Pattern. Open Journal of Discrete Mathematics, 6, 252-271.

https://doi.org/10.4236/ojdm.2016.64028