Blossoming with cancellation Original Research Article

The blossoming axioms for polynomials are extended to include additional parameters along with a cancellation axiom, further unifying the theories of the multiaffine and multirational blossoms. Several parallel identities are derived that exhibit this close connection between these two distinct forms of the blossom. Divided differences are shown to be intimately related to blossoming, and formulas are presented that express the divided differences of polynomials in terms of the multiaffine blossom.