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非标准骰子的设计(Ⅰ) 被引量:3

The Design of Non-standard Dice(Ⅰ)
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摘要 在文献中,Galllan Joseph A.,Duane M.Broline和唐高华、李云慧、韦丹妮小组分别给出了所有正多面体骰子的等价设计.该文考虑与标准骰子等价的非标准的骰子,证明了有恰有两对非标准骰子与标准正四面体骰子等价,恰有九对非标准骰子与标准正八面体骰子等价. The equivalent design of all regular polyhedron dices was presented in the literature by Gallian Joseph A. , Duane M. Broline, and the group of Tang Gaohua, Li Yunhui, Wei Danni, respectively. In this paper, we consider the non-standard dices that are equivalent to the standard one, more precisely, we prove that there are exactly two pairs of non - standard dice and nine pairs of the same sort that are equivalent to a pair of standard tetrahedral dice and regular octahedron dice respectively.
出处 《广西师范学院学报(自然科学版)》 2012年第2期21-24,共4页 Journal of Guangxi Teachers Education University(Natural Science Edition)
基金 广西自然科学基金(2010GXNSFB013048 2011GXNSFA018139) 广西教育厅科研项目(201012MS140) 广西师范学院教研教改项目((2010)22)
关键词 正四面体 正八面体 骰子 唯一分解环 投掷效果 tetrahedron octahedron dice unique factorization domain throw ef{ect
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参考文献5

  • 1LEWIS C Robertson, RAE Michael Shortt, STEPHEN G Landry. Dice with fair sums[J]. The American Mathematical Monthly, 1998, 95(4): 316-328.
  • 2JOSEPH A Gallan, DAVID J Rusin. Cyclotomic polynomials and non- standard dice[J]. Discrete Mathematics, 1979, 27 : 245-259.
  • 3GALLIAN Joseph A. Contemporary Abstract Algebra[M]. Lexington: D C Heath and Company, 1986.
  • 4DUANE M Broline. Renumbering of the face of dice[J]. Mathematics Magazine, 1979,52(5): 312-315.
  • 5唐高华,李云慧,韦丹妮.正八面体骰子的设计[J].广西师范学院学报(自然科学版),2007,24(2):16-18. 被引量:4

二级参考文献4

  • 1GARDNER M.Mathematical games[J].Scientific American,1978,238(2):19-32.
  • 2GALLIAN J A.Contemporary Abstract Algebra[M].Houghton Mifflin Company,2005.
  • 3张禾瑞.近世代数基础[M].北京:高等教育出版社,2003.
  • 4北京大学数学系几何与代数教研室代数小组.高等代数[M].2版.北京:高等教育出版社,2003.

共引文献3

同被引文献11

  • 1GALLIAN Joseph A. Contemporary Abstract Algebra[M]. Lexington: D C Heath and Company, 1986.
  • 2DUANE M Broline. Renumbering of the face of dice[J]. Mathematics Magazine, 1979, 52(5) : 312-315.
  • 3LEWIS C Robertson, RAE Michael Shortt, STEPHEN G Landry. Dice with fair sums[ J ]. The American Mathematical Monthly, 1998, 95(4): 316-328.
  • 4JOSEPH A Gallan, DAVID J Rusin. Cyclotomie polynomials and non-standard dice[J]. Discrete Mathematics, 1979, 27 : 245-259.
  • 5GALLIAN Joseph A. Contemporary Abstract Algebra[M. Lexington: D C Heath and Company, 1986.
  • 6DUANE M Broline. Renumbering of the face of dice[J]. Mathematics Magazine, 1979, 52(5) : 312-315.
  • 7LEWIS C Robertson, RAE Michael Shortt, STEPHEN G Landry. Dice with fair sums[J]. The American Mathematical Monthly, 1998, 95(4): 316-328.
  • 8JOSEPH A Gallan, DAVID J Rusin. Cyclotomic polynomials and non-standard dice[J]. Discrete Mathematics, 1979, 27: 245-259.
  • 9唐高华,李云慧,韦丹妮.正八面体骰子的设计[J].广西师范学院学报(自然科学版),2007,24(2):16-18. 被引量:4
  • 10苏华东,黄琳.非标准骰子的设计(Ⅱ)[J].广西师范学院学报(自然科学版),2012,29(3):12-14. 被引量:2

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