查看“︁希臘拉丁方陣”︁的源代码

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'''希臘拉丁方陣'''（{{lang-en|Graeco-Latin square}}）為兩個[[拉丁方陣]]相正交所得到的[[方陣]]。

<center><math>
\begin{bmatrix}
 a\beta & b\gamma & c\alpha \\
 b\alpha & c\beta & a\gamma \\
 c\gamma & a\alpha & b\beta \\
\end{bmatrix}

\begin{bmatrix}
 a\gamma & b\alpha & c\beta \\
 b\beta & c\gamma & a\alpha \\
 c\alpha & a\beta & b\gamma \\
\end{bmatrix}
</math></center>

<center>
{| class="wikitable"
|-
| 1A || 2B || 3C
|-
| 2C || 3A || 1B
|-
| 3B || 1C || 2A
|}

{| class="wikitable"
|-
| ㄅㄚ || ㄆㄞ || ㄇㄢ
|-
| ㄆㄢ || ㄇㄚ || ㄅㄞ
|-
| ㄇㄞ || ㄅㄢ || ㄆㄚ
|}
</center>

它跟[[數獨]]一樣，每一行、每一列都不會重複，並且每一個[[拉丁字母]]與每一[[希臘字母]]只配對一次，就稱這兩方陣互為[[正交]](orthogonal)，疊合後的方陣稱為希臘拉丁方陣，當n為[[質數]]或[[質數冪]]時，n階[[拉丁方陣]]有 n-1 個[[正交方陣]]（orthogonal square）；當n為[[2]]或[[6]]時，不存在n階正交方陣；而當n=[[10]]時，存在兩個正交方陣，但是是否存在三個正交方陣則未知，反倒是目前已經知道不存在九個正交方陣，[[換句話說]]，最多只能有八個正交方陣；至於n=[[12]]，則存在至少五個正交方陣，希臘拉丁方陣跟[[拉丁方陣]]一樣可以[[旋轉]]或[[翻轉]]，因為旋轉或翻轉後的結果仍然符合希臘拉丁方陣的定義。

== 多重希臘拉丁方陣 ==

三個[[拉丁方陣]]或以上相正交所得到的[[方陣]]。

以下為三重希臘拉丁方陣：

<center>
{|class="wikitable"
|林依雯
|張雅婷
|楊曉涵
|劉珮琪
|-
|劉曉婷
|楊珮雯
|張依琪
|林雅涵
|-
|張珮涵
|林曉琪
|劉雅雯
|楊依婷
|-
|楊雅琪
|劉依涵
|林珮婷
|張曉雯
|}
</center>

<center>
{|class="wikitable"
|鄭聖翰
|陳文哲
|徐明軒
|王育華
|-
|徐育哲
|王明翰
|鄭文華
|陳聖軒
|-
|陳明華
|鄭育軒
|王聖哲
|徐文翰
|-
|王文軒
|徐聖華
|陳育翰
|鄭明哲
|}
</center>

<center>
{|class="wikitable"
|呂政翔
|吳柏豪
|蕭志諺
|朱俊傑
|-
|蕭俊豪
|朱志翔
|呂柏傑
|吳政諺
|-
|朱柏諺
|蕭政傑
|吳俊翔
|呂志豪
|-
|吳志傑
|呂俊諺
|朱政豪
|蕭柏翔
|}
</center>

<center>
{| class="wikitable"
|-
| {{green|瀋陽國小}} || {{blue|忠孝國中}} || {{red|復興高中}} || {{purple|中山高工}}
|-
| {{blue|中山高中}} || {{green|復興高工}} || {{purple|忠孝國小}} || {{red|瀋陽國中}}
|-
| {{red|忠孝高工}} || {{purple|瀋陽高中}} || {{green|中山國中}} || {{blue|復興國小}}
|-
| {{purple|復興國中}} || {{red|中山國小}} || {{blue|瀋陽高工}} || {{green|忠孝高中}}
|}
</center>

以下為四重希臘拉丁方陣：

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|-
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|style="background:teal; color:lime; font-family:courier new, courier, monospace; font-weight:bold" align=center | phlegm
|style="background:navy; color:blue; font-family:comic sans ms, cursive; font-weight:bold" align=center | qiviut
|style="background:silver; color:yellow; font-family:impact, charcoal, fantasy; font-weight:bold" align=center | zincky
|-
|style="background:maroon; color:lime; font-family:comic sans ms, cursive; font-weight:bold" align=center | zincky
|style="background:teal; color:blue; font-family:impact, charcoal, fantasy; font-weight:bold" align=center | fjords
|style="background:navy; color:yellow; font-family:georgia, times, serif; font-weight:bold" align=center | jawbox
|style="background:silver; color:white; font-family:verdana, helvetica, sans-serif; font-weight:bold" align=center | phlegm
|style="background:black; color:red; font-family:courier new, courier, monospace; font-weight:bold" align=center | qiviut
|-
|style="background:teal; color:yellow; font-family:verdana, helvetica, sans-serif; font-weight:bold" align=center | qiviut
|style="background:navy; color:white; font-family:courier new, courier, monospace; font-weight:bold" align=center | zincky
|style="background:silver; color:red; font-family:comic sans ms, cursive; font-weight:bold" align=center | fjords
|style="background:black; color:lime; font-family:impact, charcoal, fantasy; font-weight:bold" align=center | jawbox
|style="background:maroon; color:blue; font-family:georgia, times, serif; font-weight:bold" align=center | phlegm
|-
|style="background:navy; color:red; font-family:impact, charcoal, fantasy; font-weight:bold" align=center | phlegm
|style="background:silver; color:lime; font-family:georgia, times, serif; font-weight:bold" align=center | qiviut
|style="background:black; color:blue; font-family:verdana, helvetica, sans-serif; font-weight:bold" align=center | zincky
|style="background:maroon; color:yellow; font-family:courier new, courier, monospace; font-weight:bold" align=center | fjords
|style="background:teal; color:white; font-family:comic sans ms, cursive; font-weight:bold" align=center | jawbox
|-
|style="background:silver; color:blue; font-family:courier new, courier, monospace; font-weight:bold" align=center | jawbox
|style="background:black; color:yellow; font-family:comic sans ms, cursive; font-weight:bold" align=center | phlegm
|style="background:maroon; color:white; font-family:impact, charcoal, fantasy; font-weight:bold" align=center | qiviut
|style="background:teal; color:red; font-family:georgia, times, serif; font-weight:bold" align=center | zincky
|style="background:navy; color:lime; font-family:verdana, helvetica, sans-serif; font-weight:bold" align=center | fjords
|}

[[Category:组合数学]]