另请参阅
列凸多联骨牌、
凸多联骨牌、
多米诺骨牌、
七联骨牌、
六联骨牌、
网格多边形、
一联骨牌、
八联骨牌、
五联骨牌、
Polyabolo、
多立方体、
多形体、
多边形六边形、
多边形菱形、
多联骨牌平铺、
Polyplet、
行凸多联骨牌、
自避多边形、
四联骨牌、
三联骨牌
使用 探索
参考文献
Atkin, A. O. L. and Birch, B. J. (Eds.). Computers in Number Theory: Proc. Sci. Research Council Atlas Symposium No. 2 Held at Oxford from 18-23 Aug., 1969. New York: Academic Press, 1971.Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 109-113, 1987.Beeler, M. Item 112 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, pp. 48-50, Feb. 1972. http://www.inwap.com/pdp10/hbaker/hakmem/polyominos.html#item112.Beineke, L. W. and Wilson, R. J. (Eds.). Selected Topics in Graph Theory. New York: Academic Press, pp. 417-444, 1978.Berge, C.; Chen, C. C.; Chvátal, V.; and Seow, C. S. "Combinatorial Properties of Polyominoes." Combin. 1, 217-224, 1981.Berlekamp, E. R.; Conway, J. H; and Guy, R. K. Winning Ways for Your Mathematical Plays, Vol. 1: Adding Games, 2nd ed. Wellesley, MA: A K Peters, 1982.Berlekamp, E. R.; Conway, J. H; and Guy, R. K. Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, 1982.Bousquet-Mélou, M.; Guttmann, A. J.; Orrick, W. P.; and Rechnitzer, A. "Inversion Relations, Reciprocity and Polyominoes." 23 Aug 1999. http://arxiv.org/abs/math.CO/9908123.Clarke, A. L. "Polyominoes." http://www.recmath.com/PolyPages/PolyPages/Polyominoes.html.Conway, A. R. and Guttmann, A. J. "On Two-Dimensional Percolation." J. Phys. A: Math. Gen. 28, 891-904, 1995.Eden, M. "A Two-Dimensional Growth Process." Proc. Fourth Berkeley Symposium Math. Statistics and Probability, Held at the Statistical Laboratory, University of California, June 30-July 30, 1960. Berkeley, CA: University of California Press, pp. 223-239, 1961.Finch, S. R. "Klarner's Polyomino Constant." §5.19 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 378-382, 2003.Gardner, M. "Mathematical Games: About the Remarkable Similarity between the Icosian Game and the Towers of Hanoi." Sci. Amer. 196, 150-156, May 1957.Gardner, M. "Polyominoes and Fault-Free Rectangles." Ch. 13 in Martin Gardner's New Mathematical Diversions from Scientific American. New York: Simon and Schuster, pp. 150-161, 1966.Gardner, M. "Polyominoes and Rectification." Ch. 13 in Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 172-187, 1978.Golomb, S. W. "Checker Boards and Polyominoes." Amer. Math. Monthly 61, 675-682, 1954.Golomb, S. W. Polyominoes: Puzzles, Patterns, Problems, and Packings, 2nd ed. Princeton, NJ: Princeton University Press, 1995.Goodman, J. E. and O'Rourke, J. (Eds.). Handbook of Discrete & Computational Geometry. Boca Raton, FL: CRC Press, 1997.Keller, M. "Counting Polyforms." http://members.aol.com/wgreview/polyenum.html.Klarner, D. A. "Cell Growth Problems." Can. J. Math. 19, 851-863, 1967.Klarner, D. A. and Riverst, R. "A Procedure for Improving the Upper Bound for the Number of 
-ominoes." Can. J. Math. 25, 585-602, 1973.
Lei, A. "Bigger Polyominoes." http://www.cs.ust.hk/~philipl/omino/bigpolyo.htmlLei, A. "Polyominoes." http://www.cs.ust.hk/~philipl/omino/omino.htmlLunnon, W. F. "Counting Polyominoes." In Computers in Number Theory (Ed. A. O. L. Atkin and B. J. Brich). London: Academic Press, pp. 347-372, 1971.Lunnon, W. F. "Counting Hexagonal and Triangular Polyominoes." In Graph Theory and Computing (Ed. R. C. Read). New York: Academic Press, 1972.Madachy, J. S. "Pentominoes: Some Solved and Unsolved Problems." J. Rec. Math. 2, 181-188, 1969.Martin, G. Polyominoes: A Guide to Puzzles and Problems in Tiling. Washington, DC: Math. Assoc. Amer., 1991.Marzetta, A. "List of Polyominoes of order 4..7." http://wwwjn.inf.ethz.ch/ambros/polyo-list.html.Mertens, S. "Lattice Animals--A Fast Enumeration Algorithm and New Perimeter Polynomials." J. Stat. Phys. 58, 1095-1108, 1990.Montgomery-Smith, S. "Polyomino Puzzles Software." http://www.math.missouri.edu/~stephen/software/polyomino/.Myers, J. "Polyomino Tiling." http://www.srcf.ucam.org/~jsm28/tiling/.Parkin, T. R.; Lander, L. J.; and Parkin, D. R. "Polyomino Enumeration Results." SIAM Fall Meeting. Santa Barbara, CA, 1967.Putter, G. "Gerard's Universal Polyomino Solver." http://www.xs4all.nl/~gp/PolyominoSolver/Polyomino.html.Read, R. C. "Contributions to the Cell Growth Problem." Canad. J. Math. 14, 1-20, 1962.Read, R. C. "Some Applications of Computers in Graph Theory." In Selected Topics in Graph Theory (Ed. L. W. Beineke and R. J. Wilson). New York: Academic Press, pp. 417-444, 1978.Redelmeier, D. H. "Counting Polyominoes: Yet Another Attack." Discrete Math. 36, 191-203, 1981.Ruskey, F. "Information on Polyominoes." http://www.theory.csc.uvic.ca/~cos/inf/misc/PolyominoInfo.html.Schroeppel, R. Item 77 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, p. 30, Feb. 1972. http://www.inwap.com/pdp10/hbaker/hakmem/proposed.html#item77.Sloane, N. J. A. Sequences A000105/M1425, A000988/M1749, A001168/M1639, and A001419/M4226 in "The On-Line Encyclopedia of Integer Sequences."Vichera, M. "Polyforms." http://www.vicher.cz/puzzle/polyforms.htm.von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 342-343, 1993.Weisstein, E. W. "Books about Polyominoes." http://www.ericweisstein.com/encyclopedias/books/Polyominoes.html.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 117, 1991.Wells, D. Recreations in Logic. New York: Dover, 1979.在 上被引用
多联骨牌
请引用为
Weisstein, Eric W. "Polyomino." 来自 Web 资源。 https://mathworld.net.cn/Polyomino.html
学科分类
个大小相等的正方形以边重合的方式排列而成的一组图形。多联骨牌最初被 Gardner (1957) 称为“超级多米诺骨牌”。含有
个正方形的多联骨牌被称为
-多联骨牌或“
-omino。”
-三联骨牌）。4-ominoes (四联骨牌) 被称为直型、L、T、正方形和斜四联骨牌。5-ominoes (五联骨牌) 被称为
、
、
、
、
、
、
、
、
、
、
和
(Golomb 1995)。另一种常见的命名方案用
、
、
和
替换
、
、
和
，以便使用从 O 到 Z 的所有字母 (Berlekamp et al. 1982)。
的自由和固定多联骨牌的数量，Mertens (1990) 给出了一个简单的计算机程序。下表给出了前几个
的自由（Lunnon 1971, 1972；Read 1978；Redelmeier 1981；Ball 和 Coxeter 1987；Conway 和 Guttmann 1995；Goodman 和 O'Rourke 1997，第 229 页）、固定（Redelmeier 1981）和单面多联骨牌（Redelmeier 1981；Golomb 1995；Goodman 和 O'Rourke 1997，第 229 页）的数量，以及包含孔的多联骨牌的数量（Parkin et al. 1967，Madachy 1969，Golomb 1994）。
-多联骨牌数量的最佳界限是
