Chapter 9: Q63E (page 632)
To determine all compatible total ordering for the poset \((\{ 1,2,4,5,12,20\} ,)\).
Short Answer
The compatible total ordering for the poset is
\(\begin{array}{l}1 \prec 5 \prec 2 \prec 4 \prec 12 \prec 20\\1 \prec 2 \prec 5 \prec 4 < 12 \prec 20\\1 \prec 2 \prec 4 \prec 5 < 12 \prec 20\\1 \prec 2 \prec 4 < 12 < 5 < 20\\1 \prec 5 \prec 2 \prec 4 < 20 < 12\\1 \prec 2 \prec 5 < 4 < 20 < 12\\1 \prec 2 \prec 4 \prec 5 < 20 \prec 12\end{array}\)