When is an Incomplete 3 × n Latin Rectangle Completable?
We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2013-03-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1648 |
| _version_ | 1827832801966161920 |
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| author | Euler Reinhardt Oleksik Paweł |
| author_facet | Euler Reinhardt Oleksik Paweł |
| author_sort | Euler Reinhardt |
| collection | DOAJ |
| description | We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4. |
| first_indexed | 2024-03-12T05:19:59Z |
| format | Article |
| id | doaj.art-aa9b72cb0ac342edbdc964449972529c |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T05:19:59Z |
| publishDate | 2013-03-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-aa9b72cb0ac342edbdc964449972529c2023-09-03T07:47:13ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922013-03-01331576910.7151/dmgt.1648When is an Incomplete 3 × n Latin Rectangle Completable?Euler Reinhardt0Oleksik Paweł1Université Européenne de Bretagne and Lab-STICC, CNRS, UMR 6285, Université de Brest, B.P.809, 20 Avenue Le Gorgeu, 29285 Brest Cedex, FranceAGH University of Science and Technology, Faculty of Geology, Geophysics and Environment Protection, Department of Geoinformatics and Applied Computer Science, 30-059 Cracow, PolandWe use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.https://doi.org/10.7151/dmgt.1648incomplete latin rectanglecompletabilitysolution space enumerationbranch-and-bound |
| spellingShingle | Euler Reinhardt Oleksik Paweł When is an Incomplete 3 × n Latin Rectangle Completable? Discussiones Mathematicae Graph Theory incomplete latin rectangle completability solution space enumeration branch-and-bound |
| title | When is an Incomplete 3 × n Latin Rectangle Completable? |
| title_full | When is an Incomplete 3 × n Latin Rectangle Completable? |
| title_fullStr | When is an Incomplete 3 × n Latin Rectangle Completable? |
| title_full_unstemmed | When is an Incomplete 3 × n Latin Rectangle Completable? |
| title_short | When is an Incomplete 3 × n Latin Rectangle Completable? |
| title_sort | when is an incomplete 3 n latin rectangle completable |
| topic | incomplete latin rectangle completability solution space enumeration branch-and-bound |
| url | https://doi.org/10.7151/dmgt.1648 |
| work_keys_str_mv | AT eulerreinhardt whenisanincomplete3nlatinrectanglecompletable AT oleksikpaweł whenisanincomplete3nlatinrectanglecompletable |