Is there a common symbol for concatenating two (finite) sequences?

Say we have two finite sequences $X = (x_0,...,x_n)$ and $Y = (y_0,...,y_n)$. Is there a more or less common notation for the concatenation of these sequences, like $\sum (X,Y) = (x_0,...,x_n,y_0,...,y_n)$?

Solution 1:

The comments suggest the following notations for the concatenation of $X$ and $Y$:

• $X^\frown Y$ (given by X^\frown Y);
• $XY$ (given by XY);
• $X \cdot Y$ (given by X \cdot Y);
• $X \mathbin\Vert Y$ (given by X \mathbin\Vert Y);

of which the first seems not to be in use for other concepts, making it especially suitable.

Solution 2:

The same question on Tex SE.

From there, and more:

• $X \oplus Y$ (given by X \oplus Y);
• $(X,Y)$ (given by (X,Y));

I would avoid $X \times Y$, $XY$ or $X \cdot Y$ to not confuse it with any sort of multiplication / product.

And I would also not use $X \otimes Y$ because it is usually the tensor product. (See also here.)

Some relevant Wikipedia pages with common notations:

• Vector space
• Direct sum
• Tensor product

Solution 3:

$\newcommand\mdoubleplus{\mathbin{+\mkern-10mu+}}$ In haskell the $ \mdoubleplus $ operator is used for concatenating lists.

You can define it in latex using the command

\newcommand\mdoubleplus{\mathbin{+\mkern-10mu+}}