5

I'm trying to generate the following output in LaTeX: enter image description here

However I am failing pretty hard at aligning those correctly, this is what I've tried so far:

\begin{align*}
&(a)\hspace{20pt}\lfloor{n/2}\rfloor &< p &\leq\hspace{19pt} n &\Rightarrow {l}_{p}(n\wr)&=1 \\
&(b)\hspace{20pt}\lfloor{n/3}\rfloor &< p &\leq \lfloor{n/2}\rfloor &\Rightarrow {l}_{p}(n\wr)&=0 \\
&(c)\hspace{20pt}\sqrt{n} &< p &\leq \lfloor{n/3}\rfloor &\Rightarrow {l}_{p}(n\wr)&=\lfloor{n/p}\rfloor\mod 2\\
&(d)\hspace{20pt}2 &< p &\leq \sqrt{n} &\Rightarrow {l}_{p}(n\wr)&<\log_2(n)\\
&(d)\hspace{20pt}{} p &= 2 &\Rightarrow {l}_{p}(n\wr)={\sigma}_{2}(\lfloor{n/2}\rfloor)
\end{align*}

How can I do this alignment the right way as presented in the example?

4

For multiple points (and no big spacing between the blocks) there is alignat. Let's examine your problem, recalling that alignat makes pairs of “right aligned/left aligned” columns.

You have: left aligned column (for the item labels); right aligned column (for the lower bounds); left aligned column (for the relations); right aligned column (for the variable); left aligned column (for the upper bounds); column that can be either left or right aligned (the arrows); left aligned column (for the final conditions).

So we should have

&\text{(a)}\qquad
&\lfloor n/2\rfloor
&<{}
&p
&&\le n
&\implies
&l_p(n\wr)=1
\\

and we should repeat the pattern. We have a total of eight &, which makes for five pairs. The empty group after the relation is to ensure correct spacing. I use \implies that adds some space at either end by itself. I took advantage from the fact that the final condition all have the same structure, so the alignment is automatic; otherwise, follow the same pattern analysis.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{alignat*}{5}
&\text{(a)}\qquad &\lfloor n/2\rfloor &<{} &p &\leq n                  &\implies &l_{p}(n\wr)=1 \\
&\text{(b)}\qquad &\lfloor n/3\rfloor &<{} &p &\leq \lfloor n/2\rfloor &\implies &l_{p}(n\wr)=0 \\
&\text{(c)}\qquad &\sqrt{n}           &<{} &p &\leq \lfloor n/3\rfloor &\implies &l_{p}(n\wr)=\lfloor n/p\rfloor \bmod 2\\
&\text{(d)}\qquad &2                  &<{} &p &\leq \sqrt{n}           &\implies &l_{p}(n\wr)<\log_2(n)\\
&\text{(e)}\qquad &                   &    &p &= 2                     &\implies &l_{p}(n\wr)=\sigma_{2}(\lfloor n/2\rfloor)
\end{alignat*}

\end{document}

I removed all the useless braces (none is needed for \lfloor x\rfloor). Note that “mod” as a binary operation should be \bmod, not \mod.

You may want to consider a space saving macro \floor:

\documentclass{article}
\usepackage{amsmath,mathtools}

\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}

\begin{document}

\begin{alignat*}{5}
&\text{(a)}\qquad &\floor{n/2} &<{} &p &\leq n           &\implies &l_{p}(n\wr)=1 \\
&\text{(b)}\qquad &\floor{n/3} &<{} &p &\leq \floor{n/2} &\implies &l_{p}(n\wr)=0 \\
&\text{(c)}\qquad &\sqrt{n}    &<{} &p &\leq \floor{n/3} &\implies &l_{p}(n\wr)=\floor{n/p} \bmod 2\\
&\text{(d)}\qquad &2           &<{} &p &\leq \sqrt{n}    &\implies &l_{p}(n\wr)<\log_2(n)\\
&\text{(e)}\qquad &            &    &p &= 2              &\implies &l_{p}(n\wr)=\sigma_{2}(\floor{n/2})
\end{alignat*}

\end{document}

enter image description here

3

For example can you use alignat instead of align. I prette printed your code to see better where the columns are. See that I doubled the last two & in each row.

MWE:

\documentclass[a4paper,12pt]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{amsmath}


\begin{document}

\begin{alignat*}{5}
&(a)\hspace{20pt}\lfloor{n/2}\rfloor &< p &\leq\hspace{19pt} n      &&\Rightarrow {l}_{p}(n\wr)&&=1 \\
&(b)\hspace{20pt}\lfloor{n/3}\rfloor &< p &\leq \lfloor{n/2}\rfloor &&\Rightarrow {l}_{p}(n\wr)&&=0 \\
&(c)\hspace{20pt}\sqrt{n}            &< p &\leq \lfloor{n/3}\rfloor &&\Rightarrow {l}_{p}(n\wr)&&=\lfloor{n/p}\rfloor\mod 2\\
&(d)\hspace{20pt}2                   &< p &\leq \sqrt{n}            &&\Rightarrow {l}_{p}(n\wr)&&<\log_2(n)\\
&(d)\hspace{20pt}{} p                &= 2 &                         &&\Rightarrow {l}_{p}(n\wr)&&={\sigma}_{2}(\lfloor{n/2}\rfloor)
\end{alignat*}

\end{document}

Result:

enter image description here

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