Corn is maize by a different name - that is, apparently wheat may be called corn in America (?) but what is meant generally is sweet corn. It should only be as a treat (10% max of diet) or the hens will be missing out on the balanced nutrition of the layers pellets and, in the case of corn, it will be fattening which is not good for a layers long term health (or any chickens long term health for that matter.)
As Valerie says, good quality layers pellets and greens are all you need for the best eggs. I did worry that too many greens would dilute their nutritional intake but it doesn't seen to work that way to any noticeable extent. I think its because, although their appetite is governed by the fullness of their crop, the protein in the layers pellets is always desirable - they wont just eat the greens however much is available. This is kind of borne out by wide roaming free rangers who will be back to the feeder for what they need unless they happen to find everything they need nutritionally in the wild (which is unlikely for a hen bred to lay.)
I give mine a half an average sweetheart cabbage or a single spring green stem between 6 once a day with maybe a handful of leaves later. I try to pick the greener cabbages as (for no proven reason) greener seems better although they do like white cabbage and are not very impressed by a savoy!