Matches in SemOpenAlex for { <https://semopenalex.org/work/W2062171640> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W2062171640 endingPage "664" @default.
- W2062171640 startingPage "654" @default.
- W2062171640 abstract "Let e be a real number and S = { x 1 , … , x n } be a set of n distinct positive integers. The set S is said to be gcd-closed (respectively lcm-closed) if ( x i , x j ) ∈ S (respectively [ x i , x j ] ∈ S ) for all 1 ⩽ i , j ⩽ n . The matrix having e th power [ x i , x j ] e of the least common multiple of x i and x j as its i , j -entry is called the e th power least common multiple (LCM) matrix, denoted by ( [ x i , x j ] e ) (or abbreviated by ( [ S ] e ) ). In this paper, we show that for any real number e ⩾ 1 and n ⩽ 7 , the power LCM matrix ( [ x i , x j ] e ) defined on any gcd-closed (respectively lcm-closed) set S = { x 1 , … , x n } is nonsingular. This confirms partially two conjectures raised by Hong in [S. Hong, Nonsingularity of matrices associated with classes of arithmetical functions, J. Algebra 281 (2004) 1–14]. Similar results are established for reciprocal real number power GCD matrices." @default.
- W2062171640 created "2016-06-24" @default.
- W2062171640 creator A5023135321 @default.
- W2062171640 date "2007-09-01" @default.
- W2062171640 modified "2023-09-29" @default.
- W2062171640 title "Notes on Hong's conjectures of real number power LCM matrices" @default.
- W2062171640 cites W1495550473 @default.
- W2062171640 cites W1964823596 @default.
- W2062171640 cites W1974058718 @default.
- W2062171640 cites W1984096699 @default.
- W2062171640 cites W1993639308 @default.
- W2062171640 cites W1993888825 @default.
- W2062171640 cites W1995734876 @default.
- W2062171640 cites W2022131401 @default.
- W2062171640 cites W2036309207 @default.
- W2062171640 cites W2039655969 @default.
- W2062171640 cites W2044636635 @default.
- W2062171640 cites W2045347633 @default.
- W2062171640 cites W2066224268 @default.
- W2062171640 cites W2107125306 @default.
- W2062171640 cites W2114112633 @default.
- W2062171640 cites W2115375406 @default.
- W2062171640 cites W2150631905 @default.
- W2062171640 cites W2158184531 @default.
- W2062171640 cites W2334672987 @default.
- W2062171640 cites W2363094799 @default.
- W2062171640 cites W2893324799 @default.
- W2062171640 doi "https://doi.org/10.1016/j.jalgebra.2007.05.005" @default.
- W2062171640 hasPublicationYear "2007" @default.
- W2062171640 type Work @default.
- W2062171640 sameAs 2062171640 @default.
- W2062171640 citedByCount "26" @default.
- W2062171640 countsByYear W20621716402012 @default.
- W2062171640 countsByYear W20621716402013 @default.
- W2062171640 countsByYear W20621716402014 @default.
- W2062171640 countsByYear W20621716402015 @default.
- W2062171640 countsByYear W20621716402016 @default.
- W2062171640 countsByYear W20621716402018 @default.
- W2062171640 countsByYear W20621716402020 @default.
- W2062171640 countsByYear W20621716402022 @default.
- W2062171640 crossrefType "journal-article" @default.
- W2062171640 hasAuthorship W2062171640A5023135321 @default.
- W2062171640 hasBestOaLocation W20621716401 @default.
- W2062171640 hasConcept C102607178 @default.
- W2062171640 hasConcept C106487976 @default.
- W2062171640 hasConcept C112343008 @default.
- W2062171640 hasConcept C114614502 @default.
- W2062171640 hasConcept C118615104 @default.
- W2062171640 hasConcept C136119220 @default.
- W2062171640 hasConcept C159985019 @default.
- W2062171640 hasConcept C192562407 @default.
- W2062171640 hasConcept C202444582 @default.
- W2062171640 hasConcept C33923547 @default.
- W2062171640 hasConcept C94375191 @default.
- W2062171640 hasConcept C96442724 @default.
- W2062171640 hasConceptScore W2062171640C102607178 @default.
- W2062171640 hasConceptScore W2062171640C106487976 @default.
- W2062171640 hasConceptScore W2062171640C112343008 @default.
- W2062171640 hasConceptScore W2062171640C114614502 @default.
- W2062171640 hasConceptScore W2062171640C118615104 @default.
- W2062171640 hasConceptScore W2062171640C136119220 @default.
- W2062171640 hasConceptScore W2062171640C159985019 @default.
- W2062171640 hasConceptScore W2062171640C192562407 @default.
- W2062171640 hasConceptScore W2062171640C202444582 @default.
- W2062171640 hasConceptScore W2062171640C33923547 @default.
- W2062171640 hasConceptScore W2062171640C94375191 @default.
- W2062171640 hasConceptScore W2062171640C96442724 @default.
- W2062171640 hasIssue "2" @default.
- W2062171640 hasLocation W20621716401 @default.
- W2062171640 hasOpenAccess W2062171640 @default.
- W2062171640 hasPrimaryLocation W20621716401 @default.
- W2062171640 hasRelatedWork W2008575124 @default.
- W2062171640 hasRelatedWork W2022131401 @default.
- W2062171640 hasRelatedWork W2028291525 @default.
- W2062171640 hasRelatedWork W2062171640 @default.
- W2062171640 hasRelatedWork W2135173043 @default.
- W2062171640 hasRelatedWork W2357898102 @default.
- W2062171640 hasRelatedWork W2982419476 @default.
- W2062171640 hasRelatedWork W3032688075 @default.
- W2062171640 hasRelatedWork W3176090163 @default.
- W2062171640 hasRelatedWork W4233660220 @default.
- W2062171640 hasVolume "315" @default.
- W2062171640 isParatext "false" @default.
- W2062171640 isRetracted "false" @default.
- W2062171640 magId "2062171640" @default.
- W2062171640 workType "article" @default.