Formation of orthogonal latin squares by index structuring of n-set multiplication tables
Objective. Formation of structurally perfect orthogonal Latin squares by the method of index ordering of the multiplication table elements of n-sets based on the multiplication table. Methods. Orthogonal Latin squares are formed by the method of index structuring of n-set multiplication tables. Resu...
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| Format: | Article |
| Language: | Russian |
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Dagestan State Technical University
2020-10-01
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| Series: | Вестник Дагестанского государственного технического университета: Технические науки |
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| Online Access: | https://vestnik.dgtu.ru/jour/article/view/843 |
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| _version_ | 1849250217639018496 |
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| author | P. A. Kadiev I. P. Kadiev |
| author_facet | P. A. Kadiev I. P. Kadiev |
| author_sort | P. A. Kadiev |
| collection | DOAJ |
| description | Objective. Formation of structurally perfect orthogonal Latin squares by the method of index ordering of the multiplication table elements of n-sets based on the multiplication table. Methods. Orthogonal Latin squares are formed by the method of index structuring of n-set multiplication tables. Results. A method is proposed for constructing structurally perfect orthogonal Latin squares of pairs of indexed finite sets of odd dimension, based on the index ordering of an nxn-array of elements in the multiplication table. A distinctive feature of the proposed method for constructing structurally perfect orthogonal squares from elements of two indexed sets of the same dimension is the use by the authors of the method of permutations of elements of the original nxn-matrix configurations, with the formation of index-ordered or index-structured combinatorial configurations. Conclusion. The use of the method for constructing a family of orthogonal Latin squares for pairs of indexed finite sets of the same odd dimension by the elements forming their multiplication table by the method of index structuring based on the principle of functional dependency of the index values on pairs of set elements and index values on pairs of elements from its environment allows creating a specific class orthogonal configuration, which, in terms of element indices, easily demonstrates their orthogonality. |
| format | Article |
| id | doaj-art-7aea2a204e3c47f991cc93eba90d4128 |
| institution | Kabale University |
| issn | 2073-6185 2542-095X |
| language | Russian |
| publishDate | 2020-10-01 |
| publisher | Dagestan State Technical University |
| record_format | Article |
| series | Вестник Дагестанского государственного технического университета: Технические науки |
| spelling | doaj-art-7aea2a204e3c47f991cc93eba90d41282025-08-20T03:57:19ZrusDagestan State Technical UniversityВестник Дагестанского государственного технического университета: Технические науки2073-61852542-095X2020-10-01473718110.21822/2073-6185-2020-47-3-71-81595Formation of orthogonal latin squares by index structuring of n-set multiplication tablesP. A. Kadiev0I. P. Kadiev1Daghestan State Technical UniversityDaghestan State Technical UniversityObjective. Formation of structurally perfect orthogonal Latin squares by the method of index ordering of the multiplication table elements of n-sets based on the multiplication table. Methods. Orthogonal Latin squares are formed by the method of index structuring of n-set multiplication tables. Results. A method is proposed for constructing structurally perfect orthogonal Latin squares of pairs of indexed finite sets of odd dimension, based on the index ordering of an nxn-array of elements in the multiplication table. A distinctive feature of the proposed method for constructing structurally perfect orthogonal squares from elements of two indexed sets of the same dimension is the use by the authors of the method of permutations of elements of the original nxn-matrix configurations, with the formation of index-ordered or index-structured combinatorial configurations. Conclusion. The use of the method for constructing a family of orthogonal Latin squares for pairs of indexed finite sets of the same odd dimension by the elements forming their multiplication table by the method of index structuring based on the principle of functional dependency of the index values on pairs of set elements and index values on pairs of elements from its environment allows creating a specific class orthogonal configuration, which, in terms of element indices, easily demonstrates their orthogonality.https://vestnik.dgtu.ru/jour/article/view/843orthogonal latin squaresmultiplication tablecombinatorial configurationsindex structuring |
| spellingShingle | P. A. Kadiev I. P. Kadiev Formation of orthogonal latin squares by index structuring of n-set multiplication tables Вестник Дагестанского государственного технического университета: Технические науки orthogonal latin squares multiplication table combinatorial configurations index structuring |
| title | Formation of orthogonal latin squares by index structuring of n-set multiplication tables |
| title_full | Formation of orthogonal latin squares by index structuring of n-set multiplication tables |
| title_fullStr | Formation of orthogonal latin squares by index structuring of n-set multiplication tables |
| title_full_unstemmed | Formation of orthogonal latin squares by index structuring of n-set multiplication tables |
| title_short | Formation of orthogonal latin squares by index structuring of n-set multiplication tables |
| title_sort | formation of orthogonal latin squares by index structuring of n set multiplication tables |
| topic | orthogonal latin squares multiplication table combinatorial configurations index structuring |
| url | https://vestnik.dgtu.ru/jour/article/view/843 |
| work_keys_str_mv | AT pakadiev formationoforthogonallatinsquaresbyindexstructuringofnsetmultiplicationtables AT ipkadiev formationoforthogonallatinsquaresbyindexstructuringofnsetmultiplicationtables |