This page contains the supplementary materials referenced in the paper "Distinguishing Phylogenetic Networks."

The Macaulay2 files below contain the computations to verify the claims made in Proposition 4.4: 3LeafNetworks_AllModels.m2, Proposition 4.6: 4LeafNetworks_JC.m2, Proposition 4.7: 4LeafNetworks_CFN.m2, and Lemma 4.13: 5LeafNetworks_JC.m2.

CORRECTIONS: There was a coding error in the file 3LeafNetworks_AllModels.m2 which has been corrected. As a result, the statements concerning the 3-leaf, 3-cycle networks in Proposition 4.4 and in Example 4.10 require slight modifications.

• In Proposition 4.4, it is true that for the 3-leaf 3-cycle network there are no invariants for the CFN, JC, and K2P models, however there is a single invariant for the K3P model which is independent of the chosen labeling.
• In Example 4.10, it is not true that the there are no invariants for the 3-leaf 3-cycle with all leaf edges contracted. However, the example only requires that there are no invariants for the 3-leaf 3-cycle with any one leaf edge contracted, which is true and which is now verified in 3LeafNetworks_AllModels.m2.