Abstract
In a Coxeter group, an element is fully commutative if all its reduced expressions can be obtained each from the other by interchanges of adjacent commuting generators. These elements were extensively studied by Stembridge. Recently, Feinberg-Kim-Lee-Oh have extended the study of fully commutative elements from Coxeter groups to the complex setting, giving an enumeration of such elements in G(m,1,n). In this note, we prove a connection between fully commutative elements in Bn and in G(m,1,n), which allows us to characterize fully commutative elements in G(m,1,n) by pattern avoidance. Further, we present a counting formula for such elements in G(m,1,n).
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