Signed Tilings by Ribbon L n-Ominoes, n Even, via Gröbner Bases

Show more

References

[1] Golomb, S.W. (1954) Checker Boards and Polyominoes. American Mathematical Monthly, 61, 675-682.

http://dx.doi.org/10.2307/2307321

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

[3] Pak, I. (2000) Ribbon tile Invariants. Transactions of the American Mathematical Society, 352, 5525-5561.

http://dx.doi.org/10.1090/S0002-9947-00-02666-0

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

http://dx.doi.org/10.1016/j.disc.2012.12.007

[5] 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.

http://dx.doi.org/10.4236/ojdm.2015.52002

[6] Golomb, S.W. (1964) Replicating Figures in the Plane. Mathematical Gazette, 48, 403-412.

http://dx.doi.org/10.2307/3611700

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

[8] Conway, J.H. and Lagarias, J.C. (1990) Tilings with Polyominoes and Combinatorial Group Theory. Journal of Combinatorial Theory, Series A, 53, 183-208.

http://dx.doi.org/10.1016/0097-3165(90)90057-4

[9] Bodini, O. and Nouvel, B. (2004) Z-Tilings of Polyominoes and Standard Basis, in Combinatorial Image Analysis. Springer, Berlin, 137-150.

http://dx.doi.org/10.1007/978-3-540-30503-3_11

[10] Nitica, V. (2015) Signed Tilings by Ribbon L n-Ominoes, n Odd, via GrÖbner Bases. arXiv:1601.00558v2.

[11] Barnes, F.W. (1982) Algebraic Theory of Brick Packing I. Discrete Math, 42, 7-26.

http://dx.doi.org/10.1016/0012-365X(82)90049-8

[12] Barnes, F.W. (1982) Algebraic Theory of Brick Packing II. Discrete Math, 42, 129-144.

http://dx.doi.org/10.1016/0012-365X(82)90211-4

[13] Becker, T. and Weispfenning, V. (In Cooperation with Krendel, H.) (1993) GrÖbner Bases. Springer-Verlag, Berlin.

[14] Dizdarevic, M.M., Timotijevic, M. and Zivaljevic, R.T. (2016) Signed Polyominotilings by n-in-Line Polyominoesand GrÖbner Bases. Publications de l’Institut Mathematique, Nouvelle Série, 99, 31-42.

http://dx.doi.org/10.2298/PIM1613031M

[15] Seidenberg, A. (1974) Constructions in Algebra. Transactions of the American Mathematical Society, 197, 273-313.

http://dx.doi.org/10.1090/S0002-9947-1974-0349648-2

[16] Klarner, D.A. (1969) Packing a Rectangle with Congruent N-Ominoes. Journal of Combinatorial Theory, 7, 107-115.

http://dx.doi.org/10.1016/S0021-9800(69)80044-X

[17] Calderon, A., Fairchild, S., Nitica, V. and Simon, S. (2015) Tilings of Quadrants by L-Ominoes and Notched Rectangles. Topics in Recreational Mathematics, 5-7, 39-75.