The phrase "absolutely count on" is correct and usable in written English.
It can be used when expressing strong trust or reliance on someone or something.
Example: "You can absolutely count on me to help you with your project."
Alternatives: "completely rely on" or "totally depend on".
"He is one of the guys I know I can absolutely count on week in, week out, so I was really pleased that he is as happy with us as we are with him.
In fact, by the time I'd left for Chile, seeing new bird species was the only activity that I could absolutely count on not to bore me.
You can absolutely count on me for these five things.
"We are absolutely counting on that — for you to succeed where we have failed".
It is for these reasons, says Ganesh, that "Cameron absolutely counts on him".
If proper synchronization of sound and picture was achieved in recording, it could be absolutely counted on in playback.
Keep making the wide-reaching case that diversity is a business necessity; that the very future of our relevance absolutely counts on it.
We keep reading about the devastation caused by oil spills, natural gas "fracking," mountaintop removal coal mining, etc. because we are renting our property to bad renters -- people who aren't charged a market rate, don't give a security deposit, and who can absolutely counted on to wreck the house.
Because they are both Google-branded, they are equipped with recent versions of Android, and Google promises to update them consistently with improvements and security fixes, something you absolutely cannot count on from other vendors and the mobile carriers that sell them.
Our culture may still whisper into the ears of young women that Prince Charming will come, sweep you off your feet, and take care of you -- which is fine if it happens, enjoy the ride -- but make sure you have a Plan B, because you absolutely cannot count on happily ever after.
