  Generalising the work of Dey, we define the notion of ultra-synchronicity of
sequences of real numbers. Let $B_{n,k},C_{n,k},P_{n,k},Q_{n,k}$ 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
$n\ge 5$. This proves a strengthening of two conjectures of Dey.
