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Odd length for even hyperoctahedral groups and signed generating functions. (English) Zbl 1370.05010
Summary: We define a new statistic on the even hyperoctahedral groups which is a natural analogue of the odd length statistic recently defined and studied on Coxeter groups of types $$A$$ and $$B$$. We compute the signed (by length) generating function of this statistic over the whole group and over its maximal and some other quotients and show that it always factors nicely. We also present some conjectures.

MSC:
 05A15 Exact enumeration problems, generating functions 05A05 Permutations, words, matrices 11M41 Other Dirichlet series and zeta functions 20F55 Reflection and Coxeter groups (group-theoretic aspects)
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