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 Wolfram|Alpha 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 Wolfram|Alpha 上被引用
多联骨牌
请引用为
Weisstein, Eric W. "Polyomino." 来自 MathWorld--Wolfram 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
