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math.GR2026
A note on the scatteredness of reflection orders
Weijia Wang, Rui Wang
In this note, we characterize affine and non-affine Coxeter systems among all Coxeter systems in terms of the structure of their reflection orders. For an infinite irreducible syst…
math.GR2025
Biclosed sets, quasitrivial semigroups and oriented matroid
Weijia Wang, Rui Wang
In this paper, we establish a one-to-one correspondence between the set of biclosed sets in an irreducible root system of type and the set of quasitrivial semigroup structure…