serves as a proxy for the dense gas fraction.

Dense Gas in Other Post-Starburst-Like Galaxies
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There are two other post-starburst-like galaxies with dense gas observations in the literature. We do not include them in our analysis because they are not selected by our post-starburst selection criteria, but we discuss them here. The first is NGC 5195 (M51b). While the nucleus of this galaxy shows a post-starburst signature [spectrum from @Heckman1980], the integrated spectrum [@Kennicutt1992] does not have the significant Balmer absorption required to be selected into our sample. This galaxy was observed in CO (1–0) and HCN (1–0) by @Kohno2002 with the Nobeyama 45m. Subsequent observations by @Matsushita2010 did not detect HCN. Observations of NGC 5195 are complicated by the nearby spiral arm of M51 in this interacting system. Resolved measurements by @Kohno2002 using the Nobeyama Millimeter Array (NMA) are brighter than the 15 beam unresolved observations. @Alatalo2016a reobserved this galaxy using the Combined Array for Research in Millimeter Astronomy (CARMA) and found a CO (1–0) line flux in between the two @Kohno2002 measurements. NGC 5195 has both HCN [*and*]{} CO luminosities consistent with its SFR from @Lanz2013, unlike our targets. @Alatalo2016a conclude this galaxy has a star formation 