Determinant Representations of Sequences: A Survey
This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or non...
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De Gruyter
2014-02-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.2478/spma-2014-0005 |
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doaj-bfd046e43480437b9b692e7276b451b52021-10-02T19:17:08ZengDe GruyterSpecial Matrices2300-74512014-02-012110.2478/spma-2014-0005spma-2014-0005Determinant Representations of Sequences: A SurveyMoghaddamfar A. R.0Salehy S. Navid1Salehy S. Nima2Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, IranDepartment of Mathematics, Florida State University, Tallahassee, FL 32306, USADepartment of Mathematics, Florida State University, Tallahassee, FL 32306, USAThis is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or nonhomogeneous recurrence relations, and others are constructed by convolution of two sequences. In this article, we will illustrate the idea of these methods by constructing some integer matrices of this type.https://doi.org/10.2478/spma-2014-0005determinantgeneralized pascal triangle(quasi) toeplitz matrix(quasi) pascal-like matrixfibonacci (lucasjacobsthal and pell) sequence |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Moghaddamfar A. R. Salehy S. Navid Salehy S. Nima |
| spellingShingle |
Moghaddamfar A. R. Salehy S. Navid Salehy S. Nima Determinant Representations of Sequences: A Survey Special Matrices determinant generalized pascal triangle (quasi) toeplitz matrix (quasi) pascal-like matrix fibonacci (lucas jacobsthal and pell) sequence |
| author_facet |
Moghaddamfar A. R. Salehy S. Navid Salehy S. Nima |
| author_sort |
Moghaddamfar A. R. |
| title |
Determinant Representations of Sequences: A Survey |
| title_short |
Determinant Representations of Sequences: A Survey |
| title_full |
Determinant Representations of Sequences: A Survey |
| title_fullStr |
Determinant Representations of Sequences: A Survey |
| title_full_unstemmed |
Determinant Representations of Sequences: A Survey |
| title_sort |
determinant representations of sequences: a survey |
| publisher |
De Gruyter |
| series |
Special Matrices |
| issn |
2300-7451 |
| publishDate |
2014-02-01 |
| description |
This is a survey of recent results concerning (integer) matrices whose leading principal minors are well-known sequences such as Fibonacci, Lucas, Jacobsthal and Pell (sub)sequences. There are different ways for constructing such matrices. Some of these matrices are constructed by homogeneous or nonhomogeneous recurrence relations, and others are constructed by convolution of two sequences. In this article, we will illustrate the idea of these methods by constructing some integer matrices of this type. |
| topic |
determinant generalized pascal triangle (quasi) toeplitz matrix (quasi) pascal-like matrix fibonacci (lucas jacobsthal and pell) sequence |
| url |
https://doi.org/10.2478/spma-2014-0005 |
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AT moghaddamfarar determinantrepresentationsofsequencesasurvey AT salehysnavid determinantrepresentationsofsequencesasurvey AT salehysnima determinantrepresentationsofsequencesasurvey |
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