Odd length for even hyperoctahedral groups and signed generating functions. (English) Zbl 1370.05010

Brenti, Francesco; Carnevale, Angela

Discrete Math. 340, No. 12, 2822-2833 (2017).

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)

Keywords:

even hyperoctahedral groups; permutation statistics; signed generating functions

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