Density of Metric Small Cancellation in Finitely Presented Groups

Small cancellation groups form an interesting class with many desirable properties. It is a well-known fact that small cancellation groups are generic; however, all previously known results of their genericity are asymptotic and provide no information about “small” group presentations. In this note, we give closed-form formulas for both lower and upper bounds on the density of small cancellation presentations, and compare our results with experimental data.