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We show that the number of linear spaces on a set of $n$ points and the number of rank-3 matroids on a ground set of size $n$ are both of the form $(cn+o(n))^{n^2/6}$, where $c=e^{\sqrt{3}/2-3}(1+\sqrt{3})/2$. This is the final piece of the puzzle for enumerating fixed-rank matroids at this level of accuracy: there are exact formulas for enumeration of rank-1 and rank-2 matroids, and it was recently proved by van der Hofstad, Pendavingh, and van der Pol that for constant $r\ge 4$ there are $(e^{1-r}n+o(n))^{n^{r-1}/r!}$ rank-$r$ matroids on a ground set of size $n$.

Introduction: University and college campuses may be the last setting where it is possible to comprehensively address the health of a large proportion of the young adult population. It is important that health promoters understand the collective challenges students are facing, and to better understand the broader lifestyle behavioural patterning evident during this life stage. The purpose of this study was to examine the clustering of modifiable health-risk behaviours and to explore the relationship between these identified clusters and mental health outcomes among a large Canadian university sample., Methods: Undergraduate students (n = 837; mean age = 21 years) from the University of Toronto completed the National College Health Assessment survey. The survey consists of approximately 300 items, including assessments of student health status, mental health and health-risk behaviours. Latent class analysis was used to identify patterning based on eight salient health-risk behaviours (marijuana use, other illicit drug use, risky sex, smoking, binge drinking, poor diet, physical inactivity, and insufficient sleep)., Results: A three-class model based on student behavioural patterns emerged: "typical," "high-risk" and "moderately healthy." Results also found high-risk students reporting significantly higher levels of stress than typical students (χ2(1671) = 7.26, p < .01)., Conclusion: Students with the highest likelihood of engaging in multiple health-risk behaviours reported poorer mental health, particularly as it relates to stress. Although these findings should be interpreted with caution due to the 28% response rate, they do suggest that interventions targeting specific student groups with similar patterning of multiple health-risk behaviours may be needed.