\begin{table}%T3
  \caption{The specific binary fraction $\binfm$ as compared to the generating binary fraction $\binf$, for different the pairing functions. 
    \label{table:pf_binaryfraction} }
  \begin{tabular}{lllll}
    \hline
    \hline\noalign{\smallskip}
    Pairing & $\binfall$ & $\binf_{M_1 \approx \mmax}$ & $\binf_{M_1 \approx \mmin}$ & $\binfm = \binf$? \\
    \noalign{\smallskip}\hline
    RP         & $=$  & $>$        & $<$         & no, unless $\binf=100\%$  \\
    PCRP       & $=$  & $=$        & $=$         & yes  \\
   \noalign{\smallskip} %\hline
    PCP-I      & $=$  & $=$        & $=$         & yes  \\
    PCP-II     & $<$  & $\approx$  & $<$         & no   \\
    PCP-III    & $=$  & $=$        & $=$         & yes \\
    \noalign{\smallskip}%\hline
    SCP-I      & $=$  & $<,\approx,>$  & $<,\approx,>$ & no, unless $\binf=100\%$  \\
    SCP-II     & $<$  & $<,\approx,>$  & $<,\approx,>$ & no            \\
    SCP-III    & $=$  & $<,\approx,>$  & $<,\approx,>$ & no, unless $\binf=100\%$   \\
    \hline 
  \end{tabular}
\end{table}