التفاصيل البيبلوغرافية
| العنوان: |
Multi-latin squares |
| المؤلفون: |
James G. Lefevre, Nicholas J. Cavenagh, Carlo Hamalainen, Douglas S. Stones |
| المصدر: |
Discrete Mathematics. 311(13):1164-1171 |
| بيانات النشر: |
Elsevier BV, 2011. |
| سنة النشر: |
2011 |
| مصطلحات موضوعية: |
Discrete mathematics, SOMA, Mathematics::History and Overview, Latin square, Graeco-Latin square, Multi-latin square, Semi-latin square, Latin parallelepiped, Square (algebra), Separable space, Theoretical Computer Science, Combinatorics, symbols.namesake, Latin square property, Orthogonal array, symbols, FOS: Mathematics, Order (group theory), Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO), Square number, Mathematics |
| الوصف: |
A multi-latin square of order $n$ and index $k$ is an $n\times n$ array of multisets, each of cardinality $k$, such that each symbol from a fixed set of size $n$ occurs $k$ times in each row and $k$ times in each column. A multi-latin square of index $k$ is also referred to as a $k$-latin square. A $1$-latin square is equivalent to a latin square, so a multi-latin square can be thought of as a generalization of a latin square. In this note we show that any partially filled-in $k$-latin square of order $m$ embeds in a $k$-latin square of order $n$, for each $n\geq 2m$, thus generalizing Evans' Theorem. Exploiting this result, we show that there exist non-separable $k$-latin squares of order $n$ for each $n\geq k+2$. We also show that for each $n\geq 1$, there exists some finite value $g(n)$ such that for all $k\geq g(n)$, every $k$-latin square of order $n$ is separable. We discuss the connection between $k$-latin squares and related combinatorial objects such as orthogonal arrays, latin parallelepipeds, semi-latin squares and $k$-latin trades. We also enumerate and classify $k$-latin squares of small orders.
Comment: Final version as sent to journal |
| تدمد: |
0012-365X |
| DOI: |
10.1016/j.disc.2010.06.026 |
| URL الوصول: |
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::778a54a73c7e8e12712368ec41fa8d58 |
| Rights: |
OPEN |
| رقم الانضمام: |
edsair.doi.dedup.....778a54a73c7e8e12712368ec41fa8d58 |
| قاعدة البيانات: |
OpenAIRE |