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main.tex

@@ -149,8 +149,10 @@ However, Lemma~7 in \cite{Thorup_2008} does not generalize to all matroids and w
 
 \subsection{Support size}
 
-Recall that we construct the ideal tree packing recursively. Suppose that the ideal base packing for $M|F^*$ is has $n$ bases and let $m$ be the size of support of the optimal base packing of $M$. Then the number of bases in the ideal base packing of $M$ is $nm$. Note that $m$ is upperbounded by the size of the groundset.
-So the support size can be exponential.
+Recall that we construct the ideal base packing recursively. Suppose that the ideal base packing for $M|F^*$ is has $n$ bases and let $m$ be the size of support of the optimal base packing of $M$. Then the number of bases in the ideal base packing of $M$ is $nm$. Note that $m$ is upperbounded by the size of the groundset.
+The support size can be exponential. Consider a path with $n$ points and parallel edges. The depth of recursion can be $n-1$.
+
+Do we need all bases in the packing?
 
 \subsection{Rigidity matroids}
 \begin{conjecture}\label{conj:idealrigidbase}