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与正整数的无序分拆和有序分拆相关的一些恒等式 被引量:16

Some Identities Between Partitions and Compositions
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摘要 Agarwal在2003年给出了一个联系着正整数的无序分拆与有序分拆的恒等式.本文给出了该问题的另外的一些恒等式.此外,利用菲波拉契数讨论了将正整数n分拆成不含分部量1的有序分拆的几个组合性质. An identity between partitions and compositions was obtained by Agarwal in the year 2003. The object of this paper is to show other identities between partitions and compositions. In addition, we shall give several new combinatorial properties of the composition of n in with no part 1 appear by the Fibonacci number.
作者 郭育红
机构地区 河西学院数学系
出处 《数学学报(中文版)》 SCIE CSCD 北大核心 2007年第3期707-710,共4页 Acta Mathematica Sinica:Chinese Series
基金 四川省青年基金 四川省教育厅自然科学重点基金(RIEST-006-2)
关键词 分拆恒等式 组合性质 有序分拆 partitions identity combinatorial property compositions
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参考文献7

  • 1MacMahon P. A., Memoir on the compositions of numbers, Philos, Trans. Roy. Soc. London A, 1894, 184: 835-901.
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同被引文献68

  • 1郭育红,张先迪.关于一类不定方程的正整数解数[J].四川师范大学学报(自然科学版),2006,29(2):197-199. 被引量:12
  • 2郭育红,张先迪.整边三角形与正整数的一类分拆数[J].四川大学学报(自然科学版),2007,44(1):17-20. 被引量:4
  • 3吴树宏.A(n,k)和P(n,k)的精确公式[J].Journal of Mathematical Research and Exposition,2007,27(2):437-444. 被引量:4
  • 4曹汝成.组合数学[M].广州:华南理工大学出版社,1999.
  • 5Agarwal A K. An analogue of Euler's identity and new Combinatorial properties of n-colour compositions [ J ]. Computational andApplied Mathematics ,2003,160, ( 1 ) :9-16.
  • 6BrualdiRA.组合数学[M].冯舜玺,罗平,裴伟东,译.北京:机械工业出版社,2001.144-146.
  • 7MACMAHON P A. Memoir on the compositions of numbers[J]. Philos Trans Roy Soc, 1894(184): 835- 901.
  • 8ANDREWS G E. The theory of partitions,encyclopedia of mathematics and its applications[M]. Reading: the University of Reading press, 1976.
  • 9AGARWAL A K, ROGERS R. Identities for n-color partitions[J]. J Number Theory, 1988 (28) : 299-305.
  • 10AGARWALA K, ANDREWS G E. Rogers-Ramanujian identities for partitionswith" N copies N"[J]. J Combin Theory Ser A,1987,45(1) :40-49.

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