What is the opposite of copyright/All rights reserved?

It's not that simple. You have permission to use copyrighted items from the owner of the copyright, but does that permission include redistributing that copyrighted material? That is what you have to have. And if you do, there can be restrictions on how you distribute it, and if people you distribute to can redistribute it also.

For example, when you buy a movie on DVD, you buy it from the DVD producer, who has permission from the movie producers to distribute the movie. However, because they have permission to distribute it, you cannot distribute it yourself. You only have a license to use the movie for personal use. Other companies that redistribute the movie (like Netflix) has their own license with the movie producers that allows them to do so. That's why Netflix doesn't put movies up right away when they come out on DVD.

If you do have permission to redistribute, and that permission includes others can redistribute also, then you want to look at one of the "copyleft" licenses. "Copyleft" is not an actual thing, but just a term used for less restrictive licenses. You still own the copyrights to your creation, and those that own the copyright to the works you included still own the rights to those works, but you give permission for others to redistribute. You can dictate the terms of them redistributing (like not for commercial use, they must not change it, they have to give credit to you, etc).

Creative Commons is a popular license for what you want to do. GNU General Public License is another popular one for software. There are also many other ones out there, so be sure to research to find the one that fits what you want. And if you want, you can even go with a proprietary license.

It's not clear why you have permission from others for something. You need to be careful giving permission for your own work if you needed permission from others.

Anyway, you wouldn't really be looking for the "opposite" of copyright. You'd be looking to grant broad permission for use of your work. Many these days would use a Creative Commons License for that. And that should be easier than trying to forfeit your copyright and turn your work over to the public domain.

You need to put a "creative commons" icon at the end of your document which implies that others are free to use your project.