String C-group representations of alternating groups - Fernandes, Maria Elisa (Ars mathematica contemporanea, 2019)
We prove that for any integer ?$n \ge 12$?, and for every ?$r$? in the interval ?$\left 3, … , \lfloor \frac{n-1)}{2} \rfloor \right$, the group $A_n$? has a string ?$C$?-group representation of rank ?$r$?, and hence that the only alternating group whose set of such ranks is not an interval is ?$A_{11}$?.
Keywords: abstract regular polytopes; abstraktni regularni politopi; alternating groups; alternirajoče grupe; Coxeter groups; Coxeterjeve grupe; string C-groups; verižne C-grupe