I am told there was an invention that consisted of a cylinder located
under the seat of a bicycle which in some way got compressed air and
operated a piston so as to reduce the effort to pedal the bicycle by
34%. What can you tell me about this invention?

Maybe this "Compressed-air energy-storage bicycle"?

http://www.dself.dsl.pipex.com/MUSEUM/TRANSPORT/oddbike/oddbike.htm

There is a group of people who haven't taken physics, but like to
invent stuff. They often take an existing machine, take some energy
from it, and put it back somewhere else. Unfortunately, they often
lose more energy than they gain. Rather than saying that their
invention didn't work, they say that it was squelched, or bought up by
the oil companies.