Vexillary elements in the hyperoctahedral group
Vexillary permutations in the symmetric group are those permutations that avoid any subsequence with elements in the same relative position as 2143. The vexillary permutations have the property that any \(S_n\) Stanley symmetric function indexed by a vexillary permutation is actually a Schur function. The paper under review defines vexillary elements for the hyperoctahedral group as those for which the \(C_n\) Stanley symmetric function is actually a Schur \(Q\)-function. Taking this as a starting point, the authors then prove that vexillary elements in the hyperoctahedral group avoid any subsequence on a list of 18 separate patterns. This result was conjectured in \textit{T. K. Lam} [\(B_n\) Stanley symmetric functions, Discrete Math. 157, No. 1-3, 241-270 (1996; Zbl 0856.05095)].
scientific article; zbMATH DE number 1228565
scientific article