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Journal of the Ramanujan Mathematical Society

Volume 37, Issue 4, December 2022  pp. 411–417.

(n + t)–color analogue of Gordon's theorem

Authors:  M. Rana and S. Sharma
Author institution: School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147 004, Punjab, India.

Summary:  The generalization of the concept of successive ranks to hook differences led to the extension of the successive ranks theorem to partition identity involving hook differences. Agarwal and Andrews rephrased a special case of the partition identity involving hook differences in terms of Frobenius partitions to obtain Rogers-Ramanujan identities for partitions with n + t copies of n. In this paper, we generalize these identities to obtain (n + t)–color analogue of Gordon's theorem. We further invoke the special case of the partition identity on hook differences involving quintuple product to obtain n–color partitions for a quintuple product arising in an identity due to Sills.

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