# How to properly sort and name variables / parameters in mathematical papers? [closed]

I have the following question. I am in the process of finalizing my model for my first paper. I have a question about the naming or sorting of the variables / parameters. I have now labeled all decision variables with lowercase letters and the parameters with uppercase letters and Greek letters. Is there a general rule on how to name everything? And if I now present my parameters / variables in a list, I would of course sort them alphabetically. How do I then handle Greek letters? Are they then sorted according to the normal letters or are they integrated into the normal letters.

F.e:

• a
• d
• z
• ⁠β
• λ

or

• a
• ⁠β
• d
• λ
• z

In general I think it is sufficient to introduce variable names in the text without a separate list of variable names. In my opinion such a list makes sense only for notation-heavy books where the definition of the variables can be very far from where they are used.

Having said that, I suggest you separate Greek from Latin letters, since they also have a distinct semantic role in your paper (distinguishing decision variables from parameters).

There is no universally accepted convention on that, but there are a few common sense rules that can facilitate the reading.

1. Each letter should be used for just one quantity (at least locally).

2. Quantities with similar meanings should be denoted by similar letters. Similarity may mean many things: a group of the letters in the same (lower/upper) case close to each other in the same alphabet (like $a,b,c,d$) or similar letters from alphabets used in parallel (like $a,\alpha$), etc.

3. Quantities with drastically different meanings (like a set of vectors and a real number) should be denoted by different type letters (like $\mathcal V$ for the first and $\alpha$ for the second.

4. If you have various constants denoted by $c$ and $C$ (with indices or without them), as it is common in mathematical articles, it helps if you use the lowercase letter for small ones and the uppercase letters for large ones, so $c_1n\le f(n)\le C_2n^2$ reads better than $C_1 n\le f(n)\le c_2n^2$, say

Ideally, when trying to comprehend your notation, the reader should be able to quickly build a set of conditional reflexes in his/her mind, so that it would become possible to determine the type of object by its name without scrolling back to the formal definitions too often.

Note that some of those reflexes are their already: $e$ normally stands for the Euler's constant, $\pi$ for the Archimedes one, $i$ for the imaginary unit, $f$ for a function, etc. But $e$ can also be used for an edge in a graph (provided you write $e^x$ as $\exp(x)$ if it also occurs in your paper), $\pi$ can be a permutation, $i$ an index of summation and $f$ a face of a polyhedron. So, you can override the defaults to a certain extent if you do not use them simultaneously with your overrides too often.

I'm not sure why you might want to sort your variables except, perhaps, for the notation list, but even then I would rather group them like

We denote the decision parameters by lowercase letters from the beginning of the Latin alphabet ($a,b,c,\dots$)

We denote the output variables by lowercase letters from the end of the Latin alphabet ($z,y,x,\dots$)

We denote various numeric parameters by lowercase Greek letters ($\alpha,\beta,\dots$)

We denote functions by the capital letters from the middle of the Latin alphabet ($F,G,H,\dots$)

and so on.

In reality, almost no one goes that far, but having something like that in mind when you design your notation and sticking to it most of the time really helps the reader.

One can expand this list of the "unwritten rules" to infinity, but I hope you got the general idea by now, so I'll stop here.