Using greek characters in commands' arguments without braces

Question

First I want to make clear that I'm a LaTeX beginner, so I'll be detailed because I just have no clue about the origin of my problem. I'm using TeXstudio 2.12.6

I'll provide context: I have been researching how to write greek characters directly in the math mode and having them recognised as so when compiled. I.e., I wanted

α = xy^2 + β

being recognised exactly as

\alpha = xy^2 + \beta

Ι finally figured out here how to achieve it: Type Greek letters in Math Mode using Greek keyboard, just using the preamble indicated there (it's in the accepted answer):

\documentclass[a4paper,10pt]{report}
\usepackage[utf8]{inputenc}
\usepackage[greek,spanish]{babel}
\usepackage{amsmath,amssymb,dsfont,alphabeta}

\usepackage[LGR,T1]{fontenc}

Although there's some differences between the original one given in the answer and mine here:

1. the babel package flags were originally [english, greek], while mine here are [greek,spanish]: Order in the flags matters and this way spanish is the principal language in my code (as I wanted it to be).
2. I'm using {amsmath,amssymb,dsfont} too.
3. I'm using report instead of article.

Now my problem: Recently I've discovered that in math mode when using commands it's not necessary to use braces to encapsulate arguments. In other words, TeXstudio does identify \binom a b exactly as \binom{a}{b}. BUT, when I use a greek letter in an argument given without braces, it won't compile and pops up this two errors:

Package inputenc Error: Unicode char �\endgroup (U+3CE)(inputenc) not set up for use with LaTeX. \binom α

Package inputenc Error: Keyboard character used is undefined(inputenc) in inputencoding `utf8'. \binom α

When writing \binom α b in math mode.

Another example: It happens a similar thing when writing overbrace β instead of overbrace{β} in math mode. (In both cases, overbrace{β} and binom{α}{b} do work).

Please help. And thank you in advance.

Answer 1

You simply can't get what you'd like. You have to consider that \binom takes two arguments and, if a brace doesn't follow, the first argument will be the next token; similarly for the second argument.

Analysis

When you type \binom α b, TeX actually sees

\binom <CE><B1> b

so it does the same as if it had found

\binom{<CE>}{<B1>} b

where <CE> and <B1> represent characters with the indicated hexadecimal code. Remember that TeX doesn't really know about Unicode and UTF-8.

The character α is represented in UTF-8 by two bytes (the ones I showed above). The inputenc package makes <CE> into an active character, whose action is to examine the next byte and take the appropriate action, in this case, being followed by <B1> it changes the two bytes into \alpha that the package alphabeta has redefined to give

\TextOrMath{\textalpha}{\mathalpha}

So, if α appears in math mode, you'll eventually find the same as if typing \alpha in the traditional setup.

But the important fact is that <CE> must be followed by another byte so that their combination points to the right definition. Which doesn't happen if you have \binom α b.

Conclusion

Always type braces in that situation. You gain nothing by typing \binom n k instead of the clearer \binom{n}{k}.

And if you try $X_\notin$, you'll learn to also type $X_{1}. A good editor will do that for you.

Addendum: the whole story

Actually the whole thing is a bit more complicated, even the explanation above is substantially correct. If you want to know the whole story, here it is.

Following the expansion of \binom, the input \binom α b is transformed into

\genfrac (){0pt}{}<CE><B1> b

and \genfrac is a four argument macro, that in turn calls \@genfrac and the input becomes

\@genfrac\relax\@@abovewithdelims{(){0pt}} <CE><B1> b

and finally, since \@genfrac is a five argument macro, this becomes

{\relax{\begingroup <CE>\endgroup\@@abovewithdelims()0pt <B1>}} b

As you see <CE> is followed by \endgroup and, indeed, the error message is

! Package inputenc Error: Unicode char ?\endgroup (U+3CE)
(inputenc)                not set up for use with LaTeX.

(the question mark represents the prefix <CE>). After some other errors you get the same as \binom{}{b}, but the fact that b appears in the right place is just because of how TeX attempts error recovery for the missing \endgroup (that had already been absorbed and discarded in the process of expanding <CE>).