The normal ceiling and floor functions, denoted $\lceil x \rceil$ and $\lfloor x \rfloor$ respectively, refer to the smallest integer greater than or equal to $x$, and similar for the floor function.

I have a need for some notation to represent the smallest integer strictly greater than $x$, or similar for 'strict floor'.

I've had a google and nothing came up, and I'd prefer not to make up notation if some already exists. Has anyone come across notation for this before?