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Just like when we add, the parameters are called "addends", and how division has a "dividend", "divisor", "quotient", and "remainder", what is the conventional name for the n and r in combinatorics functions nCr and nPr?

Not looking for a definition (eg, the number of items chosen as a subset from all the choices). Looking for the precise term.

Intuitively I might call the r a "selector", but I have no idea if that's the right term.

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    $\begingroup$ I'm not aware of any. $\endgroup$
    – Qiaochu Yuan
    Feb 1 at 20:49
  • $\begingroup$ nice one ! let's take something simpler, $1 + x + x^2+...+ x^k+...+x^n $, then n is called degree. What's the name of k ? $\endgroup$
    – Boyku
    Feb 1 at 21:38
  • $\begingroup$ @Boyku exponent or power? $\endgroup$
    – Benjamin Wang
    Feb 1 at 21:43
  • $\begingroup$ Choosing is subtraction. Given the combinatorial context, the subtraction becomes much much more dificult combinatorics.fandom.com/wiki/Subtraction_Tables : minuend and subtrahend. $\endgroup$
    – Boyku
    Feb 1 at 21:55

2 Answers 2

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In section 5.1 Basic Identities in Concrete Mathematics by R.L. Graham, D.E. Knuth and O. Patashnik the authors introduce binomial coefficients and designate $n$ and $r$
\begin{align*} \binom{n}{r}={}_{n}C_{r} \end{align*} upper index and lower index.

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These are called indices of the symbol for the combinatorial quantity. Binomial coefficients are usually written using the notation $\binom nk$, in which one can refer to $n$ as the upper index and $k$ as the lower index. If a number like a Stirling number is written like $s(n,k)$ one could call them first and second indices. As for notations in which numbers are written around a central letter in all kinds of directions like the planets of Jupiter, just say no.

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