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.
Contents
Full-Text PDF