Abstract
We use the q-binomial theorem to prove three new polynomial identities involving q-trinomial coefficients. We then use summation formulas for the q-trinomial coefficients to convert our identities into another set of three polynomial identities, which imply Capparelli’s partition theorems when the degree of the polynomial tends to infinity. This way we also obtain an interesting new result for the sum of the Capparelli’s products. We finish this paper by proposing an infinite hierarchy of polynomial identities.
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Berkovich, A., Uncu, A.K. (2021). Elementary Polynomial Identities Involving q-Trinomial Coefficients. In: Alladi, K., Berndt, B.C., Paule, P., Sellers, J.A., Yee, A.J. (eds) George E. Andrews 80 Years of Combinatory Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-57050-7_11
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DOI: https://doi.org/10.1007/978-3-030-57050-7_11
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-57049-1
Online ISBN: 978-3-030-57050-7
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