The numbering of and references to the subsections of a given section should only use subsection numbers

Question

I have an article with multiple sections. Say Section 1 and Section 2, with subsections for each. But I want one section, say Section 2 here, to be treated specially. This question has two parts.

1. For section 2, I want the counter to just return the subsection number, i.e. instead of 2.3 I just want 3.
2. I want the section numbering to also only use the subsection numbers.

The reason for this is that this is a Notes section, so is treated specially. See the illustration below.

\documentclass{article}
\begin{document}

\section{Section one}\label{one}

See Note~\ref{note.three}. % First part of question. How can I make this read "See Note 3." not "See Note 2.3."?

\section{Notes}\label{notes}
\subsection{First note}\label{note.one} % Second part of question. How can I make this read "1 First note" not "2.1 First note"?
Some text.
\subsection{Another note}\label{note.two} % Ditto
Some more text.
\subsection{Yet another note}\label{note.three} % Ditto
Yet more text.
\end{document}

Answer 1

You can redefine the subsection counter for the special section and then redefine it again to its default behaviour after this section:

\documentclass{article}
\begin{document}

\section{Section one}\label{one}

See Note~\ref{note.three}.

\renewcommand\thesubsection{\arabic{subsection}}
\section{Notes}\label{notes}
\subsection{First note}\label{note.one}
Some text.
\subsection{Another note}\label{note.two}
Some more text.
\subsection{Yet another note}\label{note.three}
Yet more text.

\renewcommand\thesubsection{\thesection.\arabic{subsection}}
\section{Section three}
\subsection{A subsection}

\end{document}

Another option would be to use the chngcntr package and its \counterwithout (before the special section), \counterwithin (after the special section) commands:

\documentclass{article}
\usepackage{chngcntr}

\begin{document}

\section{Section one}\label{one}

See Note~\ref{note.three}.

\counterwithout{subsection}{section}
\section{Notes}\label{notes}
\subsection{First note}\label{note.one}
Some text.
\subsection{Another note}\label{note.two}
Some more text.
\subsection{Yet another note}\label{note.three}
Yet more text.

\counterwithin{subsection}{section}
\section{Section three}
\subsection{A subsection}

\end{document}

Answer 2

First off, I can't help but observe that you're running the risk of greatly confusing your readers if you have sections numbered 1, 2, ... as well as (within one section only) subsections numbered 1, 2, ... I'm afraid that the fact that LaTeX typesets section headings in \Large and subsection headings in \large is not going to help dispel the confusion to any significant degree.) You may be better off using an enumerate environment in the Notes section, and then referring to the \items within the enumerate environment.

However, if you must use subsection numbering without prefixing the corresponding section's number, you can do so by typing

\begingroup
\renewcommand{\thesubsection}{\arabic{subsection}}

at the start of the zone with the new numbering scheme, and typing

\endgroup

at the end of the zone.

Given the concerns I expressed earlier, you may want to switch to "alphabetic" or "roman" rather than "arabic" numbering for this special zone. E.g., if you typed

\renewcommand{\thesubsection}{(\alph{subsection})}

you'd get subsection "numbers" typeset as (a), (b), ..., and cross-references to these subsections would also be typeset as (a), (b), etc.