let $E$ be a n-dimensional vector space.
the exterior product of a $k-$form $\alpha$ with a $l-$form $\beta$ is the $(k+l)-$ form given by the formula :
$$\frac{1}{k ! l!} \sum_{\sigma \in S_{k+l}} \text{sign}(\sigma)\alpha(x_{\sigma(1),\cdots,x_ \sigma(k)})\beta(x_{\sigma(k+1),\cdots,x_ \sigma(k+l)})$$
where $S_{k+l}$ denotes the permutation group of $\{1,\cdots,k+l\}$
this is a definition the teacher gave to the class of last year, this year he totally omitted totally the $\frac{1}{k! l!}$ and after some googling I've defintions with in addition to the $\frac{1}{k! l!}$ there's a ($k+l) !$ on top.
my question is : which defintion is correct or which definition is most used ?
thanks !