I am writing a theorem, and in it, I mix $\frac ab$ and $a/b $. The reason for this is that I find
$$\lceil a/b \rceil \tag{1}$$
better-looking than:
$\displaystyle \biggr \lceil \frac ab \biggr \rceil \tag{2}$
or
$\displaystyle \lceil \frac ab \rceil \tag{3}$
or
$$\textstyle \lceil \frac ab \rceil \tag{4}$$
$(2)$ looks weirdly proportioned, and in $(3)$, the ceiling function is too small for the fraction. In $(4)$, the fraction is well-proportioned, but a bit small, making it harder to read. In addition, when used with $\displaystyle \frac ab$, it will lead to differing sizes of the terms, which lookes a bit weird to me. Example: $\displaystyle \frac ab – \textstyle \lceil \frac ab \rceil$.
However, I find $\frac ab$ better-looking than $a/b$, and also easier to read, as I'm not too used to using and reading the slash as a divider. This leads me to mix the two types of dividers. Whenever there's a ceiling/floor function involved, I use the slash, and when there's not, I use the fraction. So my question is, is this common and accepted? Using the $\div$ is apparently not common and "accepted", and since there seems to be a consensus on that, I suspect there may be a consensus on mixing types of notation. If there isn't a consensus, then this question does not have an objective answer other than "there is no consensus" or "there is no consensus, but the majority of papers (…)". If that's the case, I'll accept the answer.
EDIT: The context is me writing an applied math paper (applied to the field of organic chemistry). It involves combinatorics and number theory.
Best Answer
Per Section 13.10 of the AMS Style Guide:
and
So while I'm not sure there's any convention specifically for fractions within a floor/ceiling, generally speaking you're free to typeset fractions either way, to maximize legibility and tidiness of the expression, on a case-by-case basis.