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Volumn 306, Issue 19-20, 2006, Pages 2515-2528

Hex and combinatorics

Author keywords

Game of Hex

Indexed keywords

GAME THEORY; NUMERICAL ANALYSIS; NUMERICAL METHODS;

EID: 33748753764     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2006.01.029     Document Type: Article
Times cited : (24)

References (51)
  • 1
    • 33748752576 scopus 로고    scopus 로고
    • V. Anshelevich, The game of Hex: an automatic theorem proving approach to game programming, Proceedings of the 17th National Conference on AI (AAAI-2000), 2000, pp. 189-194.
  • 2
    • 33748744491 scopus 로고    scopus 로고
    • V. Anshelevich. The game of Hex: the hierarchical approach, July 2000. 〈http://www.msri.org/publications/ln/msri/2000/gametheory/anshelevich/1/〉.
  • 4
    • 0036146051 scopus 로고    scopus 로고
    • A hierarchical approach to computer Hex
    • (Also in: J. Schaeffer and J. Van den Herik, (Eds). Chips, Computers and Artificial Intelligence, Elsevier, Amsterdam, 2002, pp. 141-160.)
    • Anshelevich V. A hierarchical approach to computer Hex. Artificial Intelligence 134 (2002) 101-120 (Also in: J. Schaeffer and J. Van den Herik, (Eds). Chips, Computers and Artificial Intelligence, Elsevier, Amsterdam, 2002, pp. 141-160.)
    • (2002) Artificial Intelligence , vol.134 , pp. 101-120
    • Anshelevich, V.1
  • 5
    • 33748751655 scopus 로고    scopus 로고
    • A. Beck, M.N. Bleicher, D.W. Crowe, Games, Excursions into Mathematics, Worth, New York, 1969, pp. 317-387.
  • 6
    • 33748751444 scopus 로고    scopus 로고
    • A. Beck, M.N. Bleicher, D.W. Crowe, Appendix 2000. Excursions into Mathematics: the Millennium Edition, AK Peters, Natick, 2000.
  • 7
    • 33748754825 scopus 로고    scopus 로고
    • C. Berge, L'art subtil du Hex, Manuscript, 1977.
  • 8
    • 33748745724 scopus 로고
    • Some remarks about a Hex problem
    • Klarner D. (Ed), Wadsworth International, Belmont
    • Berge C. Some remarks about a Hex problem. In: Klarner D. (Ed). The Mathematical Gardner (1981), Wadsworth International, Belmont 25-27
    • (1981) The Mathematical Gardner , pp. 25-27
    • Berge, C.1
  • 9
    • 33748750043 scopus 로고    scopus 로고
    • Y. Björnsson, R. Hayward, M. Johanson, J. van Rijswijck, Dead cell analysis in Hex and the Shannon Game, Proceedings of Graph Theory 2004, 〈http://www.cs.ualberta.ca/∼hayward/publications.html〉, to appear.
  • 11
    • 33748756320 scopus 로고    scopus 로고
    • C. Browne, Puzzle J, Abstract Games Magazine, 8:21, 2001. Solution in C. Browne, Puzzle J, Abstract Games Magazine, 10:28, 2002.
  • 12
    • 33748752762 scopus 로고    scopus 로고
    • B. Enderton, Answers to infrequently asked questions about the game of Hex. 1995. 〈http://www.cs.cmu.edu/∼hde/hex/hexfaq/〉.
  • 13
    • 33748743601 scopus 로고
    • A winning opening in reverse Hex
    • Evans R.J. A winning opening in reverse Hex. J. Recreational Math. 7 3 (1974) 189-192
    • (1974) J. Recreational Math. , vol.7 , Issue.3 , pp. 189-192
    • Evans, R.J.1
  • 14
    • 0017007606 scopus 로고
    • A combinatorial problem which is complete in polynomial space
    • Even S., and Endre Tarjan R. A combinatorial problem which is complete in polynomial space. J. Comput. Mach. 23 (1976) 710-719
    • (1976) J. Comput. Mach. , vol.23 , pp. 710-719
    • Even, S.1    Endre Tarjan, R.2
  • 15
    • 0003385412 scopus 로고
    • The game of Hex and the Brouwer fixed point theorem
    • Gale D. The game of Hex and the Brouwer fixed point theorem. Amer. Math. Monthly 86 10 (1979) 818-827
    • (1979) Amer. Math. Monthly , vol.86 , Issue.10 , pp. 818-827
    • Gale, D.1
  • 16
    • 33748756573 scopus 로고    scopus 로고
    • D. Gale, February 2000, private communication.
  • 17
    • 27844453327 scopus 로고
    • Mathematical games
    • August 120-127; October 130-138
    • Gardner M. Mathematical games. Sci. Amer. 197 (1957) 145-150 August 120-127; October 130-138
    • (1957) Sci. Amer. , vol.197 , pp. 145-150
    • Gardner, M.1
  • 18
    • 33748757136 scopus 로고    scopus 로고
    • M. Gardner, The game of Hex, The Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, New York, 1959, pp. 73-83.
  • 19
    • 0000870032 scopus 로고
    • Mathematical games
    • Gardner M. Mathematical games. Sci. Amer. 205 1 (1961) 148-168
    • (1961) Sci. Amer. , vol.205 , Issue.1 , pp. 148-168
    • Gardner, M.1
  • 20
    • 33748757491 scopus 로고    scopus 로고
    • R.B. Hayward, A note on domination in Hex. January 2003. Manuscript 〈http://www.cs.ualberta.ca/∼hayward/publications.html〉.
  • 21
    • 33748742335 scopus 로고    scopus 로고
    • R.B. Hayward, Berge and the art of Hex, Manuscript, 2003, in: J.A. Bondy/V. Chvátal (Eds.), A biography of Claude Berge, Princeton University Press, Princeton, NJ, 〈http://www.cs.ualberta.ca/∼hayward/publications.html〉, to appear.
  • 22
    • 84902462531 scopus 로고    scopus 로고
    • R.B. Hayward, Y. Björnsson, M. Johanson, M. Kan, N. Po, J. van Rijswijck, Solving 7 × 7 Hex: virtual connections and game-state reduction, in: H.J. van den Herik, H. Iida, E.A. Heinz (Eds.), Advances in Computer Games, vol. 263 of IFIP International Federation for Information Processing, Kluwer Academic Publishers, Boston, 2003, pages 261-278.
  • 24
    • 33748742138 scopus 로고    scopus 로고
    • P. Hein, Vil de laere polygon? Series of articles in Politiken newspaper, starting 26 December 1942.
  • 25
    • 33748743856 scopus 로고    scopus 로고
    • T.R. Jensen, B. Toft, Graph Colouring Problems, Winning Hex, Wiley Interscience, New York, 1995, pp. 271-275. (Chapter 17.14)
  • 26
    • 33748754156 scopus 로고    scopus 로고
    • H.W. Kuhn, S. Nasar, (Eds.), The Essential John Nash, Princeton University Press, Princeton, NJ, 2001.
  • 27
    • 33748754686 scopus 로고    scopus 로고
    • Who wins misère Hex?
    • Berlekamp E., and Rogers T. (Eds), AK Peters, Natick, MA
    • Lagarias J., and Sleator D. Who wins misère Hex?. In: Berlekamp E., and Rogers T. (Eds). The Mathemagician and Pied Puzzler (1999), AK Peters, Natick, MA 237-240
    • (1999) The Mathemagician and Pied Puzzler , pp. 237-240
    • Lagarias, J.1    Sleator, D.2
  • 28
    • 0001530822 scopus 로고
    • A solution of the Shannon switching game
    • Lehman A. A solution of the Shannon switching game. J. Soc. Indust. Appl. Math. 12 (1964) 687-725
    • (1964) J. Soc. Indust. Appl. Math. , vol.12 , pp. 687-725
    • Lehman, A.1
  • 29
    • 33748744682 scopus 로고    scopus 로고
    • T. Maarup, Hex - everything you always wanted to know about Hex but were afraid to ask. Master's Thesis, Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark, 2005.
  • 30
    • 33748741680 scopus 로고    scopus 로고
    • T. Maarup, Hex webpage. 2005 〈http://www.maarup.net/thomas/hex/〉.
  • 32
    • 33748752104 scopus 로고    scopus 로고
    • S. Meyers, 2002. private communication.
  • 33
    • 0039612424 scopus 로고
    • A Nobel prize for John Nash
    • Milnor J. A Nobel prize for John Nash. Math. Intell. 17 3 (1995) 11-17
    • (1995) Math. Intell. , vol.17 , Issue.3 , pp. 11-17
    • Milnor, J.1
  • 35
    • 33748745086 scopus 로고    scopus 로고
    • J. Nash, Some games and machines for playing them. Technical Report D-1164, Rand Corp., 1952.
  • 36
    • 33748741523 scopus 로고    scopus 로고
    • J. Nash, December 2 1999. Telephone conversation with R. Hayward and J. van Rijswijck.
  • 38
    • 33748742948 scopus 로고    scopus 로고
    • K. Noshita, Union-connections and a simple readable winning way in 7 × 7 Hex, Proceedings of the Ninth Game Programming Japan Workshop, November 12-14, 2004, pp. 72-79.
  • 39
    • 22944450349 scopus 로고    scopus 로고
    • R. Rasmussen, F. Maire, An extension of the H-search algorithm for artificial Hex players, Proceedings of the 17th Australian Joint Conference on AI, 2004, pp. 646-657.
  • 40
    • 0001673199 scopus 로고
    • Hex ist PSPACE-vollständig
    • Reisch S. Hex ist PSPACE-vollständig. Acta Inform. 15 (1981) 167-191
    • (1981) Acta Inform. , vol.15 , pp. 167-191
    • Reisch, S.1
  • 41
    • 33748740619 scopus 로고    scopus 로고
    • S. Sackson and Editors of Klutz Press, The Book of Classic Board Games, Klutz Press, Palo Alto, CA, 1991.
  • 43
    • 0007900107 scopus 로고
    • Computers and automata
    • Shannon C. Computers and automata. Proc. Inst. Radio Eng. 41 10 (1953) 1234-1241
    • (1953) Proc. Inst. Radio Eng. , vol.41 , Issue.10 , pp. 1234-1241
    • Shannon, C.1
  • 44
    • 33748753030 scopus 로고    scopus 로고
    • J. van Rijswijck, Queenbee's home page, 2000, 〈http://www.cs.ualberta.ca/∼queenbee〉.
  • 45
    • 33748750579 scopus 로고    scopus 로고
    • J. van Rijswijck, Computer Hex: Are Bees better than Fruitflies? Master's thesis, Department of Computing Science, University of Alberta, Edmonton, Canada, 2000.
  • 46
    • 33748747455 scopus 로고    scopus 로고
    • J. van Rijswijck, Search and evaluation in Hex, Technical Report, University of Alberta, 2002, 〈 http://www.cs.ualberta.ca/∼javhar/research.html〉.
  • 48
    • 33748747541 scopus 로고    scopus 로고
    • J. Yang, Jing yang's web site, 2003-2006. 〈http://www.ee.umanitoba.ca/∼jingyang〉.
  • 49
    • 33748752485 scopus 로고    scopus 로고
    • J. Yang, S. Liao, M. Pawlak, A decomposition method for finding solution in game Hex 7 × 7, in: International Conference on Application and Development of Computer Games in the 21st Century, November 2001, pp. 96-111.
  • 50
    • 33748752667 scopus 로고    scopus 로고
    • J. Yang, S. Liao, M. Pawlak, Another solution for Hex 7 × 7, Technical Report, University of Manitoba, Winnipeg, Canada, 2002, 〈http://www.ee.umanitoba.ca/∼jingyang/TR.pdf〉.
  • 51
    • 0344583769 scopus 로고    scopus 로고
    • J. Yang, S. Liao, M. Pawlak, New winning and losing positions for 7 × 7 Hex, in: Computers and Games, Lecture Notes in Computer Science, vol. 2883, Springer, Berlin, 2002, pp. 230-248.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.