[added LeftwardsSequences.fig petero@math.columbia.edu**20120207041610 Ignore-this: 52875158a0d4cdd9d462cdc52f3c7f52 ] hunk ./Associahedron.tex 714 -\begin{figure} - \centering -% \input{LeftwardsSequence} - \caption{\textbf{Leftwards sequence}. - \label{fig:Leftwards} - Here is a leftwards sequence starting from the tree on the left..} -\end{figure} - - hunk ./Associahedron.tex 725 +\begin{figure} + \centering + \input{LeftwardsSequences} + \caption{\textbf{Leftwards sequence}. + \label{fig:Leftwards} + We have exhibited here three leftwards sequences terminating in + reducible pairs. Initial tree pairs are in the leftmost column, + and later elements of the leftwards sequence are labelled. (The + first sequence has length one, the second two have length two. The + second sequence could have been continued further.) Reducing + edge pairs are drawn thicker.} +\end{figure} + hunk ./Associahedron.tex 779 -\begin{figure} - \centering -% \input{ReduciblePair} - \caption{\textbf{Leftwards sequence}. - \label{fig:ReduciblePair} - A the left is a pair of trees which is not a reducible pair; at the right is a reducible pair. The - reducing edge pair is drawn darker.} -\end{figure} - addfile ./draws/LeftwardsSequences.fig hunk ./draws/LeftwardsSequences.fig 1 +#FIG 3.2 +Portrait +Center +Metric +A6 +30.0 +Single +-2 +1200 2 +4 0 1 100 1 0 24.0 0.0 4 500.0 250.0 10125 5850 2\001 +4 0 1 100 1 0 24.0 0.0 4 500.0 250.0 7200 5850 1\001 +4 0 1 100 1 0 24.0 0.0 4 500.0 250.0 13275 2475 2\001 +4 0 1 100 1 0 24.0 0.0 4 500.0 250.0 9900 2475 1\001 +4 0 1 100 1 0 24.0 0.0 4 500.0 250.0 10125 -675 1\001 +6 10800 -2475 450 -225 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 3 + 450 -2025 675 -1575 900 -2025 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 675 -1575 1800 -900 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1800 -900 1350 -1575 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1800 -900 1800 -1575 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1800 -900 2250 -1575 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1800 -900 2700 -1575 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 3 + 1800 -900 2250 -225 3600 -1125 +6 6750 -2475 4050 -225 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 4050 -1125 5400 -225 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5400 -225 4500 -1125 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5400 -225 5850 -1125 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5850 -1125 4950 -1575 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5850 -1125 6300 -1575 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 -1575 5850 -2025 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 -1575 6300 -2025 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 -2025 6075 -2475 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 -2025 6525 -2475 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 -1575 6750 -2025 +-6 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 10350 -1575 10800 -2025 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 10350 -2025 10575 -2475 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 10350 -2025 10125 -2475 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 10350 -1575 10350 -2025 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 10350 -1575 9900 -2025 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9900 -1125 10350 -1575 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9900 -1125 9000 -1575 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 -225 9900 -1125 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9000 -450 8550 -1125 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 8100 -1125 9000 -450 +2 1 0 7 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9000 -450 9450 -225 +2 1 0 7 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 675 -1575 1800 -900 +-6 +2 1 0 7 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1800 6300 1575 4950 +2 1 0 7 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9000 5625 9450 6300 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 9450 4050 9675 4500 9900 4050 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 9900 5400 9450 6300 8775 5175 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 9675 4500 9450 4950 9000 4500 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 4950 9000 5625 +6 7425 4050 6300 6300 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 6975 5400 6750 6300 6300 5400 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6975 5400 7425 4950 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 6750 4500 6750 4950 6300 4500 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 6525 4050 6750 4500 6975 4050 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6750 4950 6975 5400 +-6 +6 4725 4500 3600 6300 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 4050 4500 4275 4950 4500 4500 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 4275 4950 4275 5400 3825 4950 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 4275 5400 4725 4950 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 3 + 4275 5400 4050 6300 3600 5400 +-6 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 3 + 1575 4950 1800 6300 2700 4950 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1575 4950 2250 4500 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1575 4950 1800 4500 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 3 + 900 4500 1575 4950 1350 4500 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 1800 7200 900 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 1800 6750 900 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 1800 6300 900 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 6300 1800 5850 900 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5850 2250 6300 1800 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5850 2250 5400 1800 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5400 2700 5850 2250 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 5400 2700 4950 2250 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 4950 3150 5400 2700 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 4500 2700 4950 3150 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 1350 9000 450 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 1350 9675 450 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 1350 10350 450 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 1350 9900 1800 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 8100 2700 8550 3150 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 8550 3150 9000 2700 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9000 2700 8550 2250 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9000 2700 9450 2250 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 2250 9000 1800 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9450 2250 9900 1800 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 9900 1800 10800 900 +2 1 0 7 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2700 2250 2250 3150 +2 1 0 7 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 12600 1800 13050 2250 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 13500 1800 14400 900 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 13050 2250 13500 1800 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 13050 2250 12150 1350 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 12600 2700 13050 2250 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 12600 2700 12150 2250 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 12150 3150 12600 2700 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 11700 2700 12150 3150 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 13050 1350 12600 1800 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 13050 1350 13950 450 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 13050 1350 13275 450 +2 1 0 3 1 0 100 1 -1 6.40 0 0 12 0 0 2 + 13050 1350 12600 450 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2250 3150 4050 2250 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2700 2250 3150 1800 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2700 1800 2925 1125 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2700 1800 2475 1125 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2700 2250 2700 1800 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2700 2250 2250 1800 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 2250 3150 2700 2250 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 1350 2250 2250 3150 +2 1 0 3 4 0 100 1 -1 6.40 0 0 12 0 0 2 + 900 2250 2250 3150