We obtain connection coefficients between q-binomial and q-trinomial
coefficients. Using these, one can transform q-binomial identities into a
q-trinomial identities and back again. To demonstrate the usefulness of this
procedure we rederive some known trinomial identities related to partition
theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which
have recently arisen in their study of the ϕ2,1 and ϕ1,5
perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate