Recursions for Excedance Number in Some Permutations Groups
نویسندگان
چکیده
The excedance number for Sn is known to have an Eulerian distribution. Nevertheless, the classical proof uses descents rather than excedances. We present a direct recursive proof which seems to be folklore and extend it to the colored permutation groups Gr,n. The generalized recursion yields some interesting connection to Stirling numbers of the second kind. We also show some logconcavity result concerning a variant of the excedance number. Finally, we show that the generating function of the excedance number defined on Gr,n is symmetric.
منابع مشابه
Recursions for Excedance Number in Some Permutations Groups
We present recursions for the number of excedances in Coxeter groups of type A and B, as well as in the colored permutation groups Zr ≀ Sn. The proofs use only computations of excedances.
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تاریخ انتشار 2008