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Let $x = (x_i)_{i=1}^n \in \mathbb{R}^{n}$ be a vector. I would like to know if there is a compact (and common) notation for the vector $[x_1,\ldots, x_{l-1},x_{l+1},\ldots,x_n]\in \mathbb{R}^{n-1}$, that is $x$ without the element in the $l$-th position ?

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    I like $\pi_{-l}(x)$ (because $\pi_i$ is common for the $i$th projection). – 2017-02-01
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    That's nice because it can be used to delete more than one elements using the multi-index notation. – 2017-02-01

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Let $I := \{1,\ldots,n\}$ for some $n \in \mathbb{N}$. Then you could use $$x = (x_i)_{i \in I \setminus \{j\}} \in \mathbb{R}^{n-1}$$ for $j \in I$.

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I can't remember where but I have seen a notation where you write the vector $(x_1,...\hat{x_i},...,x_n)$ where the hat means to omit $x_i.$

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    I think this notation is commonly used in differential geometry ; for example in *Introduction aux variétés différentielles* by J. Lafontaine. – 2017-02-01
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    That's nice but I would hope for something more compact. – 2017-02-01