Why do we use the same notation for an array/matrix as we do for combinations? Is it just a convenient notation, or is there some deeper link with calculations using matrices? Does it have links with expanding combinations into multiple dimensions?
2026-05-14 22:51:01.1778799061
Why is the notation $\binom nr$ used for $n$ choose $r$?
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Wikipedia attributes the invention of this notation to Austrian mathematician Andreas von Ettinghausen, in the 1826 book "Die combinatorische Analysis als Vorbereitungslehre zum Studium der theoretischen höhern Mathematik". In the references section, they qoute (and, conveniently, translate) his introduction of the symbol:
The only explicit reasoning presented here is that it's convenient for frequent use (presumably that it's easy to type, read, and recognize). He does not, as far as I can see, hint at any reasoning that connects it to a matrix in any deeper way. However, I do not speak enough German to tell conclusively from the original text.