On the number of additive permutations and Skolem-type sequences
| العنوان: | On the number of additive permutations and Skolem-type sequences |
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| المؤلفون: | Diane Donovan, Mike J. Grannell |
| المصدر: | Ars Mathematica Contemporanea. 14:415-432 |
| بيانات النشر: | University of Primorska Press, 2017. |
| سنة النشر: | 2017 |
| مصطلحات موضوعية: | Combinatorics, Discrete mathematics, Algebra and Number Theory, Transversal (geometry), Modulo, Discrete Mathematics and Combinatorics, Order (group theory), Geometry and Topology, Type (model theory), Skolem sequence, Theoretical Computer Science, Mathematics |
| الوصف: | Cavenagh and Wanless recently proved that, for sufficiently large odd n , the number of transversals in the Latin square formed from the addition table for integers modulo n is greater than (3.246) n . We adapt their proof to show that for sufficiently large t the number of additive permutations on [− t , t ] is greater than (3.246) 2 t + 1 and we go on to derive some much improved lower bounds on the numbers of Skolem-type sequences. For example, it is shown that for sufficiently large t ≡ 0 or 3 (mod 4) , the number of split Skolem sequences of order n = 7 t + 3 is greater than (3.246) 6 t + 3 . This compares with the previous best bound of 2 ⌊ n /3⌋ . |
| تدمد: | 1855-3974 1855-3966 |
| DOI: | 10.26493/1855-3974.1098.ca0 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::5726b23596d55d34ec914ad6789219b4 https://doi.org/10.26493/1855-3974.1098.ca0 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi...........5726b23596d55d34ec914ad6789219b4 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 18553974 18553966 |
|---|---|
| DOI: | 10.26493/1855-3974.1098.ca0 |