Elementary Polynomial Identities Involving q-Trinomial Coecients

We use the q-binomial theorem to prove three new polynomial identities involving q-trinomial coecients. We then use summation formulas for the q-trinomial coecients to convert our identities into another set of three polynomial identities, which imply Capparellis partition theorems when the degree of the polynomial tends to innity. This way we also obtain an interesting new result for the sum of the Capparellis products. We nish this paper by proposing an innite hierarchy of polynomial identities.(VLID)4914740Version of recor