Zhu, Guangyan On the divisibility among power GCD and power LCM matrices on gcd-closed sets. (English) Zbl 1496.11047 Int. J. Number Theory 18, No. 7, 1397-1408 (2022). Reviewer: Jorma K. Merikoski (Tampere) MSC: 11C20 11A05 15B36 PDFBibTeX XMLCite \textit{G. Zhu}, Int. J. Number Theory 18, No. 7, 1397--1408 (2022; Zbl 1496.11047) Full Text: DOI
Feng, Yulu; Qiu, Min; Zhu, Guangyan; Hong, Shaofang Divisibility among power matrices associated with classes of arithmetic functions. (English) Zbl 1497.11066 Discrete Math. 345, No. 10, Article ID 112993, 11 p. (2022). Reviewer: Jorma K. Merikoski (Tampere) MSC: 11C20 15B36 11A25 PDFBibTeX XMLCite \textit{Y. Feng} et al., Discrete Math. 345, No. 10, Article ID 112993, 11 p. (2022; Zbl 1497.11066) Full Text: DOI
Zhao, Jianrong; Chen, Long; Hong, Shaofang GCD-closed sets and divisibility of Smith matrices. (English) Zbl 1484.11095 J. Comb. Theory, Ser. A 188, Article ID 105581, 23 p. (2022). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 11A05 PDFBibTeX XMLCite \textit{J. Zhao} et al., J. Comb. Theory, Ser. A 188, Article ID 105581, 23 p. (2022; Zbl 1484.11095) Full Text: DOI
Chen, Long; Hong, Shaofang Divisibility among determinants of power matrices associated with integer-valued arithmetic functions. (English) Zbl 1489.15014 AIMS Math. 5, No. 3, 1946-1959 (2020). MSC: 15A15 15B36 11C20 11A25 11N64 PDFBibTeX XMLCite \textit{L. Chen} and \textit{S. Hong}, AIMS Math. 5, No. 3, 1946--1959 (2020; Zbl 1489.15014) Full Text: DOI
Haukkanen, Pentti; Tóth, László Inertia, positive definiteness and \(\ell_p\) norm of GCD and LCM matrices and their unitary analogs. (English) Zbl 1403.15027 Linear Algebra Appl. 558, 1-24 (2018). Reviewer: Yansheng Wu (Nanjing) MSC: 15B36 11C20 11A25 11N37 PDFBibTeX XMLCite \textit{P. Haukkanen} and \textit{L. Tóth}, Linear Algebra Appl. 558, 1--24 (2018; Zbl 1403.15027) Full Text: DOI arXiv Link
Aistleitner, Christoph; Larcher, Gerhard; Lewko, Mark Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems. (English) Zbl 1388.11043 Isr. J. Math. 222, No. 1, 463-485 (2017). Reviewer: Peter Bundschuh (Köln) MSC: 11K06 11K60 PDFBibTeX XMLCite \textit{C. Aistleitner} et al., Isr. J. Math. 222, No. 1, 463--485 (2017; Zbl 1388.11043) Full Text: DOI arXiv
Hu, Shuangnian; Lian, Dongyan; Diao, Tianbo; Liu, Jing Further results on generalized LCM matrices. (English) Zbl 1389.11075 Wuhan Univ. J. Nat. Sci. 22, No. 1, 1-4 (2017). MSC: 11C20 11A25 15B36 15A15 PDFBibTeX XMLCite \textit{S. Hu} et al., Wuhan Univ. J. Nat. Sci. 22, No. 1, 1--4 (2017; Zbl 1389.11075) Full Text: DOI
Hong, S.; Hu, S.; Lin, Zong Bing On a certain arithmetical determinant. (English) Zbl 1399.11082 Acta Math. Hung. 150, No. 2, 372-382 (2016). MSC: 11C20 11A05 11B25 PDFBibTeX XMLCite \textit{S. Hong} et al., Acta Math. Hung. 150, No. 2, 372--382 (2016; Zbl 1399.11082) Full Text: DOI
Tan, Qianrong; Lin, Zongbing; Chen, Long Divisibility among power matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains. (English) Zbl 1378.11039 Linear Multilinear Algebra 64, No. 10, 2030-2048 (2016). MSC: 11C20 11A25 15B36 PDFBibTeX XMLCite \textit{Q. Tan} et al., Linear Multilinear Algebra 64, No. 10, 2030--2048 (2016; Zbl 1378.11039) Full Text: DOI
Wang, Bangyan; Hong, Shaofang; Li, Mao Hyperdeterminants on meet-semilattices. (English) Zbl 1368.11025 Linear Multilinear Algebra 64, No. 10, 1899-1915 (2016). Reviewer: Barbara Pekala (Rzeszów) MSC: 11C20 06A12 15A15 PDFBibTeX XMLCite \textit{B. Wang} et al., Linear Multilinear Algebra 64, No. 10, 1899--1915 (2016; Zbl 1368.11025) Full Text: DOI
Hong, Siao; Hu, Shuangnian; Hong, Shaofang Multiple gcd-closed sets and determinants of matrices associated with arithmetic functions. (English) Zbl 1419.11051 Open Math. 14, 146-155 (2016). MSC: 11C20 11A05 15B36 PDFBibTeX XMLCite \textit{S. Hong} et al., Open Math. 14, 146--155 (2016; Zbl 1419.11051) Full Text: DOI
Hu, Shuangnian; Hong, Shaofang; Zhao, Jianrong Determinants of matrices associated with arithmetic functions on finitely many quasi-coprime divisor chains. (English) Zbl 1338.15063 Appl. Math. Comput. 258, 502-508 (2015). MSC: 15B36 15A15 11A25 PDFBibTeX XMLCite \textit{S. Hu} et al., Appl. Math. Comput. 258, 502--508 (2015; Zbl 1338.15063) Full Text: DOI
Hu, Shuangnian; Hong, Shaofang Multiple divisor chains and determinants of matrices associated with completely even functions \(\pmod r\). (English) Zbl 1307.11035 Linear Multilinear Algebra 62, No. 9, 1240-1257 (2014). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 15A15 11A25 PDFBibTeX XMLCite \textit{S. Hu} and \textit{S. Hong}, Linear Multilinear Algebra 62, No. 9, 1240--1257 (2014; Zbl 1307.11035) Full Text: DOI
Hong, Shaofang; Li, Mao; Wang, Bangyan Hyperdeterminants associated with multiple even functions. (English) Zbl 1368.11024 Ramanujan J. 34, No. 2, 265-281 (2014). MSC: 11C20 11A05 15A15 15B36 PDFBibTeX XMLCite \textit{S. Hong} et al., Ramanujan J. 34, No. 2, 265--281 (2014; Zbl 1368.11024) Full Text: DOI
Zhao, Jianrong Divisibility of power LCM matrices by power GCD matrices on gcd-closed sets. (English) Zbl 1350.11042 Linear Multilinear Algebra 62, No. 6, 735-748 (2014). MSC: 11C20 11A25 15B36 PDFBibTeX XMLCite \textit{J. Zhao}, Linear Multilinear Algebra 62, No. 6, 735--748 (2014; Zbl 1350.11042) Full Text: DOI
Mattila, Mika; Haukkanen, Pentti On the positive definiteness and eigenvalues of meet and join matrices. (English) Zbl 1290.15022 Discrete Math. 326, 9-19 (2014). MSC: 15B48 05C50 15A42 PDFBibTeX XMLCite \textit{M. Mattila} and \textit{P. Haukkanen}, Discrete Math. 326, 9--19 (2014; Zbl 1290.15022) Full Text: DOI arXiv
Tan, Qianrong; Luo, Miao; Lin, Zongbing Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains. (English) Zbl 1288.15042 Appl. Math. Comput. 219, No. 15, 8112-8120 (2013). MSC: 15B36 11C20 PDFBibTeX XMLCite \textit{Q. Tan} et al., Appl. Math. Comput. 219, No. 15, 8112--8120 (2013; Zbl 1288.15042) Full Text: DOI
Tan, Qianrong; Li, Mao Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains. (English) Zbl 1339.11041 Linear Algebra Appl. 438, No. 3, 1454-1466 (2013). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 PDFBibTeX XMLCite \textit{Q. Tan} and \textit{M. Li}, Linear Algebra Appl. 438, No. 3, 1454--1466 (2013; Zbl 1339.11041) Full Text: DOI
Lin, Zongbing; Tan, Qianrong Determinants of Smith matrices on three coprime divisor chains and divisibility. (English) Zbl 1276.11044 Linear Multilinear Algebra 60, No. 4, 475-486 (2012). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 PDFBibTeX XMLCite \textit{Z. Lin} and \textit{Q. Tan}, Linear Multilinear Algebra 60, No. 4, 475--486 (2012; Zbl 1276.11044) Full Text: DOI
İpek, Ahmet Upper bounds for the condition numbers of the GCD and the reciprocal GCD matrices in spectral norm. (English) Zbl 1238.15003 Comput. Math. Appl. 63, No. 3, 645-651 (2012). MSC: 15A12 11C20 15B36 PDFBibTeX XMLCite \textit{A. İpek}, Comput. Math. Appl. 63, No. 3, 645--651 (2012; Zbl 1238.15003) Full Text: DOI
Haukkanen, Pentti A topological approach to divisibility of arithmetical functions and GCD matrices. (English) Zbl 1276.11008 Linear Multilinear Algebra 60, No. 3, 301-309 (2012). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11A25 06A06 11C20 15B36 PDFBibTeX XMLCite \textit{P. Haukkanen}, Linear Multilinear Algebra 60, No. 3, 301--309 (2012; Zbl 1276.11008) Full Text: DOI
Li, Mao; Tan, Qianrong Divisibility of matrices associated with multiplicative functions. (English) Zbl 1261.11031 Discrete Math. 311, No. 20, 2276-2282 (2011). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 11A25 PDFBibTeX XMLCite \textit{M. Li} and \textit{Q. Tan}, Discrete Math. 311, No. 20, 2276--2282 (2011; Zbl 1261.11031) Full Text: DOI
Hong, Shaofang; Loewy, Raphael Asymptotic behaviour of the smallest eigenvalue of matrices associated with completely even functions. (English) Zbl 1273.11052 Int. J. Number Theory 7, No. 6, 1681-1704 (2011). MSC: 11C20 11M41 11A05 15B36 PDFBibTeX XMLCite \textit{S. Hong} and \textit{R. Loewy}, Int. J. Number Theory 7, No. 6, 1681--1704 (2011; Zbl 1273.11052) Full Text: DOI arXiv
Xu, Jiehong; Li, Mao Divisibility among power GCD matrices and among power LCM matrices on three coprime divisor chains. (English) Zbl 1222.11043 Linear Multilinear Algebra 59, No. 7, 773-788 (2011). Reviewer: C. M. da Fonseca (Coimbra) MSC: 11C20 11A05 15B36 PDFBibTeX XMLCite \textit{J. Xu} and \textit{M. Li}, Linear Multilinear Algebra 59, No. 7, 773--788 (2011; Zbl 1222.11043) Full Text: DOI
Tan, Qianrong; Lin, Zongbing Divisibility of determinants of power GCD matrices and power LCM matrices on finitely many quasi-coprime divisor chains. (English) Zbl 1221.11002 Appl. Math. Comput. 217, No. 8, 3910-3915 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11A05 PDFBibTeX XMLCite \textit{Q. Tan} and \textit{Z. Lin}, Appl. Math. Comput. 217, No. 8, 3910--3915 (2010; Zbl 1221.11002) Full Text: DOI
Tan, Qianrong Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains. (English) Zbl 1245.11037 Linear Multilinear Algebra 58, No. 5-6, 659-671 (2010). MSC: 11C20 11A05 15B36 PDFBibTeX XMLCite \textit{Q. Tan}, Linear Multilinear Algebra 58, No. 5--6, 659--671 (2010; Zbl 1245.11037) Full Text: DOI
Yamasaki, Yoshinori Arithmetical properties of multiple Ramanujan sums. (English) Zbl 1203.11006 Ramanujan J. 21, No. 3, 241-261 (2010). Reviewer: Pentti Haukkanen (Tampere) MSC: 11A25 11C20 15B36 PDFBibTeX XMLCite \textit{Y. Yamasaki}, Ramanujan J. 21, No. 3, 241--261 (2010; Zbl 1203.11006) Full Text: DOI arXiv
Qian, Guoyou; Lu, Jingya LU-factorizations of symmetric matrices with applications. (English) Zbl 1200.11021 Asian-Eur. J. Math. 3, No. 1, 133-143 (2010). Reviewer: Sheng Chen (Harbin) MSC: 11C20 15B36 PDFBibTeX XMLCite \textit{G. Qian} and \textit{J. Lu}, Asian-Eur. J. Math. 3, No. 1, 133--143 (2010; Zbl 1200.11021) Full Text: DOI
Feng, Weiduan; Hong, Shaofang; Zhao, Jianrong Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets. (English) Zbl 1263.11042 Discrete Math. 309, No. 9, 2627-2639 (2009). MSC: 11C20 15B36 PDFBibTeX XMLCite \textit{W. Feng} et al., Discrete Math. 309, No. 9, 2627--2639 (2009; Zbl 1263.11042) Full Text: DOI
Hong, Shaofang; Zhou, Xingwang; Zhao, Jianrong Power GCD matrices for a UFD. (English) Zbl 1247.11033 Algebra Colloq. 16, No. 1, 71-78 (2009). MSC: 11C20 11A25 13F15 15B36 PDFBibTeX XMLCite \textit{S. Hong} et al., Algebra Colloq. 16, No. 1, 71--78 (2009; Zbl 1247.11033) Full Text: DOI Link
Altınışık, Ercan On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture. (English) Zbl 1216.11032 Linear Algebra Appl. 430, No. 4, 1313-1327 (2009). Reviewer: C. M. da Fonseca (Coimbra) MSC: 11C20 15A09 15A18 15B36 PDFBibTeX XMLCite \textit{E. Altınışık}, Linear Algebra Appl. 430, No. 4, 1313--1327 (2009; Zbl 1216.11032) Full Text: DOI
Hong, Shaofang Asymptotic behavior of largest eigenvalue of matrices associated with completely even functions (mod \(r\)). (English) Zbl 1172.11008 Asian-Eur. J. Math. 1, No. 2, 225-235 (2008). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15A18 15B36 PDFBibTeX XMLCite \textit{S. Hong}, Asian-Eur. J. Math. 1, No. 2, 225--235 (2008; Zbl 1172.11008) Full Text: DOI
Hong, Shaofang; Wang, Shaofang There does not exist an odd singular number of the form \(p^l qr\). (English) Zbl 1190.11019 Asian-Eur. J. Math. 1, No. 1, 77-83 (2008). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 15A15 11A25 PDFBibTeX XMLCite \textit{S. Hong} and \textit{S. Wang}, Asian-Eur. J. Math. 1, No. 1, 77--83 (2008; Zbl 1190.11019) Full Text: DOI
Hong, Shaofang; Enoch Lee, K. S. Asymptotic behavior of eigenvalues of reciprocal power LCM matrices. (English) Zbl 1186.11011 Glasg. Math. J. 50, No. 1, 163-174 (2008). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15A18 15B36 PDFBibTeX XMLCite \textit{S. Hong} and \textit{K. S. Enoch Lee}, Glasg. Math. J. 50, No. 1, 163--174 (2008; Zbl 1186.11011) Full Text: DOI
Hong, Shaofang Divisibility properties of power GCD matrices and power LCM matrices. (English) Zbl 1137.11017 Linear Algebra Appl. 428, No. 4, 1001-1008 (2008). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 PDFBibTeX XMLCite \textit{S. Hong}, Linear Algebra Appl. 428, No. 4, 1001--1008 (2008; Zbl 1137.11017) Full Text: DOI
Cao, Wei On Hong’s conjecture for power LCM matrices. (English) Zbl 1174.11030 Czech. Math. J. 57, No. 1, 253-268 (2007). MSC: 11C20 11A25 PDFBibTeX XMLCite \textit{W. Cao}, Czech. Math. J. 57, No. 1, 253--268 (2007; Zbl 1174.11030) Full Text: DOI EuDML Link
Zhao, Jianrong; Hong, Shaofang; Liao, Qunying; Shum, K. P. On the divisibility of power LCM matrices by power GCD matrices. (English) Zbl 1174.11031 Czech. Math. J. 57, No. 1, 115-125 (2007). MSC: 11C20 11A25 15B36 PDFBibTeX XMLCite \textit{J. Zhao} et al., Czech. Math. J. 57, No. 1, 115--125 (2007; Zbl 1174.11031) Full Text: DOI EuDML Link
Li, Mao Notes on Hong’s conjectures of real number power LCM matrices. (English) Zbl 1230.11036 J. Algebra 315, No. 2, 654-664 (2007). Reviewer: Pentti Haukkanen (MR2351885) MSC: 11C20 15B36 11A25 PDFBibTeX XMLCite \textit{M. Li}, J. Algebra 315, No. 2, 654--664 (2007; Zbl 1230.11036) Full Text: DOI
Hong, Shaofang; Shum, K. P.; Sun, Qi On nonsingular power LCM matrices. (English) Zbl 1140.11319 Algebra Colloq. 13, No. 4, 689-704 (2006). MSC: 11C20 11A25 PDFBibTeX XMLCite \textit{S. Hong} et al., Algebra Colloq. 13, No. 4, 689--704 (2006; Zbl 1140.11319) Full Text: DOI
Hong, Shaofang Nonsingularity of matrices associated with classes of arithmetical functions on lcm-closed sets. (English) Zbl 1131.11018 Linear Algebra Appl. 416, No. 1, 124-134 (2006). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15B36 11A25 PDFBibTeX XMLCite \textit{S. Hong}, Linear Algebra Appl. 416, No. 1, 124--134 (2006; Zbl 1131.11018) Full Text: DOI
Haukkanen, Pentti An upper bound for the \(\ell_p\) norm of a gcd-related matrix. (English) Zbl 1096.15009 J. Inequal. Appl. 2006, Article ID 25020, 6 p. (2006). Reviewer: John D. Dixon (Ottawa) MSC: 15B36 15A60 11A05 11C20 PDFBibTeX XMLCite \textit{P. Haukkanen}, J. Inequal. Appl. 2006, Article ID 25020, 6 p. (2006; Zbl 1096.15009) Full Text: DOI EuDML
Korkee, Ismo; Haukkanen, Pentti On a general form of meet matrices associated with incidence functions. (English) Zbl 1088.11019 Linear Multilinear Algebra 53, No. 5, 309-321 (2005). Reviewer: Cristinel Mortici (Targoviste) MSC: 11C20 PDFBibTeX XMLCite \textit{I. Korkee} and \textit{P. Haukkanen}, Linear Multilinear Algebra 53, No. 5, 309--321 (2005; Zbl 1088.11019) Full Text: DOI
Hong, Shaofang Nonsingularity of least common multiple matrices on gcd-closed sets. (English) Zbl 1080.11022 J. Number Theory 113, No. 1, 1-9 (2005). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 15A15 15B36 PDFBibTeX XMLCite \textit{S. Hong}, J. Number Theory 113, No. 1, 1--9 (2005; Zbl 1080.11022) Full Text: DOI
Hong, Shaofang Nonsingularity of matrices associated with classes of arithmetical functions. (English) Zbl 1064.11024 J. Algebra 281, No. 1, 1-14 (2004). Reviewer: Tom M. Apostol (Pasadena) MSC: 11C20 11A25 PDFBibTeX XMLCite \textit{S. Hong}, J. Algebra 281, No. 1, 1--14 (2004; Zbl 1064.11024) Full Text: DOI
Hong, Shaofang On the factorization of LCM matrices on gcd-closed sets. (English) Zbl 0995.15006 Linear Algebra Appl. 345, No. 1-3, 225-233 (2002). Reviewer: Rodica Covaci (Cluj-Napoca) MSC: 15A23 11C20 11A05 15B36 PDFBibTeX XMLCite \textit{S. Hong}, Linear Algebra Appl. 345, No. 1--3, 225--233 (2002; Zbl 0995.15006) Full Text: DOI Link
Hong, Shaofang On the Bourque-Ligh conjecture of least common multiple matrices. (English) Zbl 1015.11007 J. Algebra 218, No. 1, 216-228 (1999). MSC: 11C20 11A05 15B36 15A15 PDFBibTeX XMLCite \textit{S. Hong}, J. Algebra 218, No. 1, 216--228 (1999; Zbl 1015.11007) Full Text: DOI
Hong, Shaofang Lower bounds for determinants of matrices associated with classes of arithmetical functions. (English) Zbl 0932.11018 Linear Multilinear Algebra 45, No. 4, 349-358 (1999). Reviewer: Pentti Haukkanen (Tampere) MSC: 11C20 11A25 15A15 15B36 15A45 PDFBibTeX XMLCite \textit{S. Hong}, Linear Multilinear Algebra 45, No. 4, 349--358 (1999; Zbl 0932.11018) Full Text: DOI
Hong, Shaofang Bounds for determinants of matrices associated with classes of arithmetical functions. (English) Zbl 0937.15004 Linear Algebra Appl. 281, No. 1-3, 311-322 (1998). MSC: 15A15 11C20 11A25 15B36 15A45 PDFBibTeX XMLCite \textit{S. Hong}, Linear Algebra Appl. 281, No. 1--3, 311--322 (1998; Zbl 0937.15004) Full Text: DOI
Haukkanen, Pentti; Wang, Jun; Sillanpää, Juha On Smith’s determinant. (English) Zbl 0883.15002 Linear Algebra Appl. 258, 251-269 (1997). Reviewer: R.Covaci (Cluj-Napoca) MSC: 15A15 15B36 11C20 PDFBibTeX XMLCite \textit{P. Haukkanen} et al., Linear Algebra Appl. 258, 251--269 (1997; Zbl 0883.15002) Full Text: DOI
Haukkanen, Pentti; Sillanpää, Juha Some analogues of Smith’s determinant. (English) Zbl 0869.15005 Linear Multilinear Algebra 41, No. 3, 233-244 (1996). Reviewer: A.Kovačec (Coimbra) MSC: 15A15 15B36 15A22 PDFBibTeX XMLCite \textit{P. Haukkanen} and \textit{J. Sillanpää}, Linear Multilinear Algebra 41, No. 3, 233--244 (1996; Zbl 0869.15005) Full Text: DOI
Haukkanen, Pentti On meet matrices on posets. (English) Zbl 0870.15016 Linear Algebra Appl. 249, 111-123 (1996). Reviewer: Tong Wenting (Nanjing) MSC: 15B57 11C20 15A15 15A09 PDFBibTeX XMLCite \textit{P. Haukkanen}, Linear Algebra Appl. 249, 111--123 (1996; Zbl 0870.15016) Full Text: DOI
Bourque, Keith; Ligh, Steve Matrices associated with multiplicative functions. (English) Zbl 0826.15013 Linear Algebra Appl. 216, 267-275 (1995). Reviewer: Tong Wenting (Nanjing) MSC: 15B36 15A09 PDFBibTeX XMLCite \textit{K. Bourque} and \textit{S. Ligh}, Linear Algebra Appl. 216, 267--275 (1995; Zbl 0826.15013) Full Text: DOI