Conjugation of overpartitions and some applications of over q-binomial coefficients

Munagi, Augustine O. and Ngubane, Siphephelo (2023) Conjugation of overpartitions and some applications of over q-binomial coefficients. Annales Mathematicae et Informaticae, 59.. pp. 71-82. ISSN 1787-6117

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Abstract

We study the conjugation of overpartitions and give the generating function for the number of self-conjugate overpartitions of an integer. Following the recent introduction of over q-binomial coefficients, we obtain the over q-analogue of the Chu-Vandermonde identity. Consequently a new generating function for the number of overpartitions is proved. We also give a new over q-analogue of the Chu-Vandermonde identity.

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