The package ‘ia32-libs-gtk’ has been removed in Ubuntu 13.10 (I have no idea why). When you try and install it you get the error “Package ‘ia32-libs-gtk’ has no installation candidate”. It seems that most people need this ia32-libs-gtk for installing or running Adobe Air. I have found the solution is:
sudo apt-get install libgtk2.0-0:i386 libnss3-1d:i386 libnspr4-0d:i386 lib32nss-mdns libxml2:i386 libxslt1.1:i386
This got Adobe Air working on my computer but it would be good to get feedback from other people – so please leave a comment if it works for you.