I am new to writing mathematics papers, and often times I have the need to express an idea for which there is no standard mathematical convention (or if there is, may be too tedious to do formally).

Consider the following definition of a set of the $n^{th}$ root of unity, raised to the power $k \in \{0,1,2,\dots,n-1\}$. It seems natural to me to express this set in the following way

$$ \{\omega_n^k\}_{k=0}^{n-1} $$

Although, this makes me wonder when it is acceptable to use notation which is not particularly standard. At least, I have not seen the form above, but I do anticipate the meaning should be clear to the reader.

Is there a consensus or reference book for notation, or does one pick it up from the literature?

  • 1
    $\begingroup$ One picks it up via exposure, yes. Actually your example is reasonably standard. A general tip: don't be afraid to use "lowbrow" notation if it will communicate better - for example, here I'd be perfectly happy with $\{\omega_n^0, \omega_n^1, \dots, \omega_n^{n-1}\}$. $\endgroup$ – Greg Martin Mar 10 '14 at 0:08

I use (not sure if this standard in any sense) $$ \omega_n^k, ~~k = 0 \cdots n-1 $$ I assume your range of $k$ is $0$ to $n-1$ and not $n$.

  • $\begingroup$ Indeed, I require $n-1$. This is a good suggestion for the notation. $\endgroup$ – jII Mar 9 '14 at 23:45

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