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关于幂LCM矩阵非奇异性的洪猜想的注记(英文) 被引量:1

Notes on Hong's conjectures of nonsingularity of power LCM matrices
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摘要 作者研究了关于幂LCM矩阵非奇异性的两个洪绍方猜想,得到了几个非奇异性定理. In this paper, the authors study Hong's two conjectures of nonsingularity of power LCM matrices, and obtain several results on nonsingularity.
作者 吴荣军 何聪
出处 《四川大学学报(自然科学版)》 CAS CSCD 北大核心 2008年第4期719-722,共4页 Journal of Sichuan University(Natural Science Edition)
基金 新世纪优秀人才支持计划(NCET-060785)
关键词 幂LCM矩阵 倒数幂GCD矩阵 gcd封闭集 lcm封闭集 最大型因子 power LCM matrix, power reciprocal GCD matrix, gcd-closed set, lcm-closed set, greatest-type divisor
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参考文献15

  • 1Smith H J S. On the value of a certain arithmetical determinant[J]. Proc London Math Soc, 1875-1876, 7: 208.
  • 2Bourclue K, Ligh S. On GCD and LCM matrices[J]. Linear Algebra Appl, 1992, 174: 65.
  • 3Bourque K, Ligh S, Matrices associated with arithmetical functions [ J ]. Linear Multilinear Algebra, 1993, 34 : 261.
  • 4Bourque K, Ligh S. Matrices associated with classes of multiplicative functions [ J ]. Linear Algebra Appl, 1995, 216: 267.
  • 5Cao W. Remarks on a conjecture of Hong of power LCM matrices[J]. J Sichuan Univ. Nat Sci Ed, 2004, 41. 1124.
  • 6Cao W. On Hong's conjecture for power LCM matrices [J]. Czechoslovak Math J, 2007, 57: 253.
  • 7Hong S. LCM matrix on an r-fold gcd-closed set[J]. J Sichuan Univ. Nat Sci Ed, 1996, 33: 650.
  • 8Hong S. On LCM matrices on C, CD-closed sets[J]. Southeast Asian Bull Math, 1998, 22: 381.
  • 9Hong S. On the Bourque-Ligh conjecture of least common multiple matrices[J]. J Algebra, 1999, 218: 216.
  • 10Hong S. Gcd-closed sets and determinants of matrices associated with arithmetical functions[J]. Acta Arith, 2002, 101: 321.

同被引文献27

  • 1谭千蓉,林宗兵,刘浏.两个互素因子链上的幂GCD矩阵的行列式与幂LCM矩阵的行列式的整除性[J].四川大学学报(自然科学版),2009,46(6):1581-1584. 被引量:6
  • 2Bourque K,Ligh S.On GCD and LCM matrices[J].Linear Algebra Appl,1992,174:65.
  • 3Bourque K,Ligh S.Matrices associated with classes of arithmetical functions[J].Number Theory,1993,45:367.
  • 4Bourque K,Ligh S.Matrices associated with arithmetical functions[J].Linear Multilinear Algebra,1993,34:261.
  • 5Cao W.On Hongs conjecture for power LCM matrices[J].Czechoslovak Math,2007,57:253.
  • 6Codeca P,Nair M.Calculating a determinant associated with multilplicative functions[J].Boll Unione Mat Ital Sez B Artic Ric Mat,2002,5(8):545.
  • 7Feng W,Hong S,Zhao J.Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets[J].Discrete Math,2009,309:2627.
  • 8Haukkanen P,Korkee I.Notes on the divisibility of LCM and GCD matrices[J].International J Math and Math Science,2005,6:925.
  • 9He C,Zhao J.More on divisibility of determinants of LCM matrices on GCD-closed sets[J].Southeast Asian Bull Math,2005,29:887.
  • 10Hilberdink T.Determinants of multiplicative Toeplitz matrices[J].Acta Arith,2006,125:265.

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