6
$\begingroup$

I know that the notation $\binom{n}{r}$ is more standard to use since we have a $\LaTeX$ command for it while there is no such thing for $^n\mathrm{C}_r$.

Now, I'm wondering which notation do people use in general when writing by hand. Also, I researched a bit about which countries use which notation mostly but it was futile since I didn't get effective results.

I'd just like to know which notation is more used in general and whether the $^n\mathrm{C}_r$ is used anywhere outside India (I'm Indian, so I'd like to know). Also, I'd like if someone can provide me with some sort of a "poll" of which notation is more used in which countries.

P.s - I have tagged it as a soft question, so I hope this doesn't get closed as "too broad" or by any similar reason. Thanks!

$\endgroup$
5
  • 2
    $\begingroup$ There is also a discussion about the notation here. $\endgroup$ May 12, 2015 at 15:16
  • $\begingroup$ I'll answer as a comment because what I are going to say is not based on data, but in my personal experience. I'd say that $\binom nr$ is used at most contexts, but $^n\mathrm C_r$ it is usually seen only in combinatorial contexts. $\endgroup$
    – ajotatxe
    May 12, 2015 at 15:17
  • $\begingroup$ It's rare to see ${}^nC_r$ or $C_{n, r}$ outside elementary combinatorics (and you won't see it anywhere at all outside combinatorics), though I think I have seen some more advanced combinatorics papers that use $C(n, r)$. $\endgroup$
    – anomaly
    May 12, 2015 at 15:23
  • 1
    $\begingroup$ Not an answer, but $C_n^r$ and $C_r^n$ are both in use. $\endgroup$ May 12, 2015 at 15:34
  • $\begingroup$ I've seen all of the notations discussed in this thread, but certainly the most commonly used one was $\binom{n}{r}$. $\endgroup$
    – izœc
    May 13, 2015 at 9:23

4 Answers 4

5
$\begingroup$

Update I've added two more notation (seen on this site), which might be relevant. The data change afterwards, mostly in the exact matches in $\LaTeX$Search.

As others stated, I would go with $\binom{n}{r}$(probably never used different notation, although that does not mean much, since I am in math for only few years).

Although for example wiki (search for "binom") gives more options.

As to support my (as well as others) choices I can give you some numbers obtained by searching the terms here ($\LaTeX$Search) and here ($\LaTeX$SpeedSearch). Both hyperlinks link to the page claiming

The Springer LaTeX search lets you search through over 8,223,138 LaTeX code snippets to find the equation you need.

Claim

I did not check all the results, whether they really mean the binomial coefficient, so bear that in mind.

\begin{array}{|c|c|c|c|c|} \hline \text{Term} & \text{in }\TeX & \text{Search}^* & \text{SpeedSearch} \\ \hline \binom{n}{k} &\verb+\binom{n}{k}+ & 10/1464 & 323 \\ \hline \binom{n}{r} &\verb+\binom{n}{r}+ & 1/815 & 47 \\ \hline \binom{n}{2} &\verb+\binom{n}{2}+ & 13/0 & 166 \\ \hline \binom{n+1}{k} & \verb-\binom{n+1}{k}- & 0/14 & 14 \\ \hline ^nC_r & \verb+^nCr+ & 3/301 & 2 \\ \hline ^nC_k & \verb+^nC_k+ & 13/830 & 3\\ \hline ^nC_2 & \verb+^nC_2+ & 1/619 & 5 \\ \hline C_r^n & \verb+Cr^n+ & 1/189 & 74 \\ \hline C_k^n & \verb+C_k^n+ & 1/316 & 13\\ \hline C_2^n & \verb+C_2^n+ & 6/690 & 8\\ \hline C_n^r & \verb+C_n^r+ & 3/229 & 7 \\ \hline C_n^k & \verb+C_n^k+ & 11/287 & 37 \\ \hline C_n^2 & \verb+C_n^2+ & 39/1471 & 78 \\ \hline C(n,r) &\verb+C(n,r)+ & 0/1317 & 9\\ \hline C(n,k) &\verb+C(n,k)+ & 2/1432 & 32 \\ \hline C(n,2) &\verb+C(n,2)+ & 0/1771 & 4\\ \hline \end{array}

$^*$ The first number responds to the exact result appearance, the second to the similar one.

Conclusion

Personally I would not really consider the similar results for $\LaTeX$Search. Of course, this statement should be supported by going through the results (and obtaining, that most results are not binomial coefficients). Excluding those (and the $\binom{n+1}{k}$ row) out we get

\begin{array}{|c|c|c|} \hline \text{Type of notation} & \sum Search & \sum SpeedSearch \\ \hline \text{Notation } \binom{n}{x} & 24 & 536 \\ \hline \text{Different notation} & 80 & 272\\ \hline \end{array}

Note I did this mostly for fun. I think these sites have better usage then for some notational statistics.

$\endgroup$
2
  • $\begingroup$ This is exactly what I needed! Thanks! It'd have been much better if we could compare usage of notations between countries. $\endgroup$
    – notationer
    May 12, 2015 at 17:10
  • $\begingroup$ You might want to add that also n \choose k and matrix commands are used for the first notation. $\endgroup$
    – wythagoras
    May 13, 2015 at 14:28
5
$\begingroup$

I've seen ${}^n C_r$, but almost vanishingly rarely. The notation $n \choose r$ is easily the most common in my experience, but one sees $C(n, r)$ often too.

$\endgroup$
3
  • $\begingroup$ In my country, at least in highschool, no one uses the bracket notation. I bet most students wouldn't know what it means. Also, we put both the $n$ and $r$ at the right side. It'd look weird to put one on each side, at least to us. $\endgroup$
    – Hasan Saad
    May 12, 2015 at 15:27
  • $\begingroup$ @HasanSaad Interesting, what is your home country? (FWIW, I was educated in the U.S.) $\endgroup$ May 12, 2015 at 15:33
  • $\begingroup$ Lebanon, Middle East. $\endgroup$
    – Hasan Saad
    May 12, 2015 at 15:40
3
$\begingroup$

Certainly $n \choose r$, i have never seen ${}^n C_r$. Other than that i see $nCr$ as this is the standard input on a calculator

$\endgroup$
2
$\begingroup$

I think the notation $n \choose r$ is most common. I've never seen $^n C_r$, actually, but in cases that it must be written without LaTeX, I often see nCr. Another notation I sometimes see are $ C_r^n$ or $C(n,r)$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.