I've seen many signs (for instance, in subway) saying "Do not lean on door". Why is it "on door", not "on the door"? I thought "door" was always used with "the". Would "on the door" in such a context sound wrong?
Signs often have reduced grammar, as do newspaper headlines, captions of photographs, and so on. They may omit articles and auxiliary verbs, for example. We're so used to this that it might actually sound strange to use a complete sentence in such situations.