The sayings collection may be identified with Q, or with a subset of Q[1] if some (typically narrative-related) material normally assigned to Q is instead attributed to Matthew's creativity in conjunction with Luke's use of Matthew.
Alternatively, M.A.T. Linssen[8] proposes it as a variant by equating the sayings collection to the Gospel of Thomas, suggesting that Matthew and Luke worked together to write different gospels, each targeted at their own audience.