Year: 2025
Type: article
Abstract: 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 ΓW .In particular, we show that the number of Boolean intervals of rank k is i k (ΓW ) • |W | / 2 k , where i k (ΓW ) is the number of independent sets of size k in ΓW .Specializing to type An, we recover work of Tenner [J.Combin.13 (2022) 135-165], as well as Elder, Harris, Kretschmann, and Martínez 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.
Source: Discrete Mathematics Letters
Authors: Ben Adenbaum, Jennifer Elder, Pamela E. Harris, J. Carlos Martínez Mori
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Award: G4223229909
OpenAlex ID: W4410131440