3

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. enter image description here

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 enter image description here.

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
3

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}

enter image description here

2

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).

enter image description here

1

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}

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