In a mathematical context (explaining a formula just written) the following seems unobjectionable: "The set of unitary polynomials has been denoted by P". My question is whether it sounds right to skip the preposition "by", so that the sentence would read: "The set of unitary polynomials has been denoted P".
It's a standard passive voice construction, whereby
Of course, people tend to shorten things: the form “denoted P” is actually used both in oral and writing, but is the minority according to a couple of quick Google Scholar searches: “is denoted by x” vs. “is denoted x”.
I found both correct.