Counting Boolean intervals in the weak Bruhat order of a finite Coxeter group

Given a finite Coxeter system (W, S), we enumerate Boolean intervals in its weak Bruhat order by expressing them in terms of independent sets in its Coxeter graph W .In particular, we show that the number of Boolean intervals of rank kwhere i k (W ) is the number of independent sets of size k in W .Specializing to type An, we recover work of Tenner [J.Combin.13 (2022) 135-165], as well as Elder, Harris, Kretschmann, and Martnez Mori [J.Combin.16 (2025) 65-89].We derive analogous specialized results for types Cn and Dn, together with related generating functions and new connections to known integer sequences.