# Definition:Latin Square/Element

## Definition

Let $\mathbf L$ be a Latin square of order $n$.

The individual $n \times n$ symbols that go to form $\mathbf L$ are known as the **elements** of $\mathbf L$.

The element at row $i$ and column $j$ is called **element $\left({i, j}\right)$ of $\mathbf L$**, and can be written $a_{i j}$, or $a_{i, j}$ if $i$ and $j$ are of more than one character.

If the indices are still more complicated coefficients and further clarity is required, then the form $a \left({i, j}\right)$ can be used.

Note that the first subscript determines the row, and the second the column, of the Latin square where the element is positioned.

### Index of Element

Let $\mathbf L$ be a Latin square of order $n$.

Let $a_{i j}$ be an element of $\mathbf L$.

Then the subscripts $i$ and $j$ are referred to as the **indices** (singular: **index**) of $a_{i j}$.

## Also denoted as

Some sources prefer to use the uppercase form of the letter for the element:

- $ A_{i j}$

## Also known as

The **elements of a Latin Square** are sometimes seen as **entries of a Latin Square**.