Author:
Berkovich Alexander,Uncu Ali Kemal
Abstract
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.
Funder
Johannes Kepler University Linz
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics
Reference17 articles.
1. Andrews, G.E.: Euler’s “exemplum memorabile inductionis fallacis” and $$q$$-trinomial coefficients. J. Amer. Math. Soc. 3(3), 653–669 (1990)
2. Andrews, G.E.: Schur’s theorem, Capparelli’s conjecture and $$q$$-trinomial coefficients. In: Andrews, G.E., Bressoud, D.M., Parson, L.A. (eds.) The Rademacher Legacy to Mathematics (University Park, PA, 1992), Contemp. Math., 166, pp. 141–154. Amer. Math. Soc., Providence, RI (1994)
3. Andrews, G.E.: The Theory of Partitions. Cambridge University Press, Cambridge (1998)
4. Andrews, G.E.: Rogers-Ramanujan polynomials for modulus 6. In: Berndt, B.C., Diamond, H.G., Hildebrand, A.J. (eds.) Analytic Number Theory, Vol. 1 (Allerton Park, IL, 1995), Progr. Math., 138, pp. 17–30. Birkhäuser Boston, Boston, MA (1996)
5. Andrews, G.E.: $$q$$-Trinomial coefficients and Rogers-Ramanujan type identities. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds.) Analytic Number Theory (Allerton Park, IL, 1989), Progr. Math., 85, pp. 1–11. Birkhäuser Boston, Boston, MA (1990)
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