Let h:ZβZβ₯0β be a nonzero function with h(k)=0
for kβͺ0. We define the quasi depth of h by qdepth(h)=max{d:βjβ€kβ(β1)kβj(kβjdβjβ)h(j)β₯0Β forΒ allΒ kβ€d}.
We show that qdepth(h) is a natural generalization for the quasi depth of a
subposet Pβ2[n] and we prove some basic properties of it.
Given h(j)=ajp+b, jβ₯0, with a,b,n positive integers, we compute
qdepth(h) for n=1,2 and we give sharp bounds for qdepth(h) for pβ₯3.
Also, for h(j)=anβjn+β―+a1βj+a0β, jβ₯0, with aiββ₯0, we prove
that qdepth(h)β€2n+1.Comment: 18 page