# Symbol Request: Poset relation with dot inside

When dealing with posets, it's common to denote the fact that some object x is smaller than some object y using the notation

x \preceq y


An image of the symbol is given.

However, if y is the smallest such element larger than x (we say that y "covers" x), it's common to place a dot inside of the sideways V such as in .

Is there a code for such a symbol? I tried drawing this in Detexify, but I had no luck.

• if this is a common notation, can you give a reference to a published example? (it is best if the example shows the symbol in context and with a clear definition of its meaning.) with such a reference, i am willing to submit it to be considered for addition to unicode. – barbara beeton Aug 25 '17 at 15:13

If there is not any, why don't you define one?

\documentclass{article}

\usepackage{amsmath}

\newcommand\preceqdot{\mathrel{\ooalign{$\preceq$\cr
\hidewidth\raise0.225ex\hbox{$\cdot\mkern0.5mu$}\cr}}}

\begin{document}

$x \preceq y$, $x \preceqdot y$
{\large $x \preceq y$ $x \preceqdot y$}
{\Large $x \preceq y$ $x \preceqdot y$}
{\LARGE $x \preceq y$ $x \preceqdot y$}
{\huge $x \preceq y$ $x \preceqdot y$}
{\Huge $x \preceq y$ $x \preceqdot y$}

\end{document}


The height of the centered dot is good for making up the symbol with \prec; we can use this fact for computing the amount of raising needed for \preceq.

\documentclass{article}

\newcommand{\precdot}{\prec\mathrel{\mkern-5mu}\mathrel{\cdot}}

\makeatletter
\newcommand{\preceqdot}{\mathrel{\mathpalette\pr@ceqd@t\relax}}
\newcommand{\pr@ceqd@t}[2]{%
\begingroup
\sbox\z@{$#1\prec$}\sbox\tw@{$#1\preceq$}%
\dimen@=\dimexpr\ht\tw@-\ht\z@\relax
{\preceq}%
\mkern-5mu
\raisebox{\dimen@}{$\m@th#1\cdot$}%
\endgroup
}
\makeatother

\begin{document}

$a\precdot b_{\precdot}$

$a\preceqdot b_{\preceqdot}$

\end{document}


Depending on your preferences, you can change the amount of backspacing (now 5mu).

If you need this symbol only in text style and display style, you can define

\def\preceqdot{\mathrel{\preceq\kern-.5em\raise.22ex\hbox{$\cdot$}}}


If you will use it in other math styles, the definition is slight more complicated:

\newcount\stylenum
\def\varstyle#1{\mathchoice{\stylenum=0 #1}{\stylenum=1 #1}{\stylenum=2 #1}{\stylenum=3 #1}}
\def\usestyle{\ifcase\stylenum\displaystyle\or\textstyle\or\scriptstyle\or\scriptscriptstyle\fi}

\def\preceqdot{\mathrel{\varstyle{\preceq\prcdkern\prcdraise\hbox{$\usestyle\cdot$}}}}
\def\prcdkern{\kern-.\ifcase\stylenum 5\or 5\or 2\or 2\fi em}
\def\prcdraise{\raise.\ifcase\stylenum 22\or 22\or 17\or 14\fi ex}