Why in this sentence past participle goes without auxiliary verb?
The table painted red, the sofa covered with American leather of a reddish colour with little green flowers on it, and the clothes taken off in haste overnight
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Your examples are reduced relative clause constructions. "the table painted red" is from "the table which is/was painted red" by deleting the "which is" part. The deletion transformation has been called "WHIZ".
In turn, for this example, the "is/was" is part of a passive construction, the active form for which would be "someone paints/painted the table red". Whether the interpretation is present or past tense depends on the context the construction occurs in.
Try putting the description before the subject. "The painted red table was there", "taken off in haste clothes were lying on the floor". The point of the sentence is not description, it's something else or just the subject. And the participle is just additional information we happen to put after it. I don't really know the words that could explain it in terms of grammar but hope it helps.