Synchronicity of descent and excedance enumerators in the alternating subgroup

Generalising the work of Dey, we define the notion of ultra-synchronicity of sequences of real numbers. Let Bn,k,Cn,k,Pn,k,Qn,k be the number of even permutations with k descents, odd permutations with k descents, even permutations with k excedances and odd permutations with k excedances respectively. We show that the four sequences are ultra-synchronised for all n≥ 5. This proves a strengthening of two conjectures of Dey.