Did Matthew Know Luke? A Neglected Angle on the Synoptic Problem

I was going to call this something like “Taking another Luke at the Synoptic Problem”, but I thought I might have reached my pun quota already. But I’ve often wondered why the possibility that Matthew might have used Luke’s Gospel as a source is rarely even mentioned in books on and discussions of the Synoptic Problem. Perhaps it is simply the fact that Luke is traditionally dated relatively late, or perhaps it is the fact that Luke’s reference to “many” who had already written before him ought to include Matthew (and who knows what else).

But if one wishes to eliminate the hypothetical Q source (which I don’t, I might add), the only plausible way to do so would seem to me to be by arguing that Matthew used Luke, rather than vice versa. In almost all cases, Luke’s order and shorter form of Q material appears more original.

So what do you think? (My blog is looking at your blog as it says this, Mark Goodacre, in case you couldn’t tell). Why is this option regularly omitted, or if mentioned not explored in detail? Can anyone recommend a good treatment of the topic, whether it comes down in favor of Matthean dependence on Luke or the Q hypothesis?