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GCD封閉集上冪矩陣行列式的整除性

2023-04-29 13:14:05朱光艷強詩瑗林宗兵
關(guān)鍵詞:行列式矩陣文獻

朱光艷 強詩瑗 林宗兵

參考文獻:

[1] ??Smith ?H J S. On the value of a certain arithmetical determinant [J]. Proc London Math Soc, 1875-1876, 7: 208.

[2] ?Apostol T M. Arithmetical properties of generalized Ramanujan sums [J]. Pacific J Math, 1972, 41: 281.

[3] ?Bourque ?K, Ligh S. On GCD and LCM matrices [J]. Linear Algebra Appl, 1992, 174: 65.

[4] ?Bourque K, Ligh S. Matrices associated with classes of arithmetical functions [J]. J Number Theory, 1993, 45: 367.

[5] ?Bourque K, Ligh S. Matrices associated with arithmetical functions [J]. Linear Multilinear Algebra, 1993, 34: 261.

[6] ?Chen L, Feng Y L, Hong S F, ?et al . On the divisibility of matrices associated with multiplicative functions [J]. Publ Math Debrecen, 2022, 100: 323.

[7] ?Chen L, Hong S F. Divisibility among determinants of power matrices associated with integer-valued arithmetical functions [J]. AIMS Math, 2020, 5: 1946.

[8] ?Hong ?S F. On Bourque-Ligh conjecture of least common multiple matrices [J]. J Algebra, 1999, 218: 216.

[9] ?Hong S F. Gcd-closed sets and determinants of matrices associated with arithmetical functions [J]. Acta Arith, 2002, 101: 321.

[10] ?Hong S F. Factorization of matrices associated with classes of arithmetical functions [J]. Colloq Math, 2003, 98: 113.

[11] Hong ?S F. Non-singularity of matrices associated with classes of arithmetical functions [J]. J Algebra, 2004, 281: 1.

[12] Tan Q R, Lin Z B. Divisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chains [J]. Appl Math Comput, 2010, 217: 3910.

[13] Zhao J R, Chen L, Hong S F. Gcd-closed sets and divisibility of Smith matrices [J]. J Comb Theory Ser A, 2022, 188: 105581.

[14] Zhu G Y, Li M, Tan Q R. Divisibility among determinants of power matrices on gcd-closed sets [J]. J Sichuan Univ: Nat Sci Ed, 2021, 58: 061005.

[15] Zhu G Y. On the divisibility among power GCD and power LCM matrices on gcd-closed sets [J]. Int J Number Theory, 2022, 18: 1397.

[16] Zhu G Y, Li M. On the divisibility among power LCM matrices on gcd-closed sets [J]. Bull Aust Math Soc, 2023, 107: 31.

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