Year: 1395
Publish place: Transactions on Combinatorics، Vol: 5، Issue: 2
COI: JR_COMB-5-2_005
Language: EnglishView: 34
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Abstract:
Two Latin squares of order n are orthogonal if in their superposition, each of the n^{۲} ordered pairs of symbols occurs exactly once. Colbourn, Zhang and Zhu, in a series of papers, determined the integers r for which there exist a pair of Latin squares of order n having exactly r different ordered pairs in their superposition. Dukes and Howell defined the same problem for Latin squares of different orders n and n+k. They obtained a non-trivial lower bound for r and solved the problem for k \geq \frac{۲n}{۳} . Here for k < \frac{۲n}{۳}, some constructions are shown to realize many values of r and for small cases (۳\leq n \leq ۶), the problem has been solved.
Keywords:
Latin square , Orthogonal Latin square , r-Orthogonal Latin square , r-Orthogonality spectrum , Transversal
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لیست زیر مراجع و منابع استفاده شده در این Paper را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود Paper لینک شده اند :- G. B. Belyavskaya, r-Orthogonal quasigroups I, Math. Issled., ۳۹ (۱۹۷۶) ...
- G. B. Belyavskaya, r-Orthogonal quasigroups II, Math. Issled., ۴۳ (۱۹۷۶) ...
- G. B. Belyavskaya, r-Orthogonal Latin squares, in: J. Dénes and ...
- C. J. Colbourn and L. Zhu, The spectrum of r-orthogonal ...
- P. Dukes and J. Howell, The orthogonality spectrum for Latin ...
- J. Howell, The intersection problem and different pairs problem for ...
- H. J. Ryser, A combinatorial theorem with an application to ...
- L. Zhu and H. Zhang, A few more r-orthogonal Latin ...
- L. Zhu and H. Zhang, Completing the spectrum of r-orthogonal ...
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