Journal of the Ramanujan Mathematical Society

Volume 37, Issue 4, December 2022 pp. 419–435.

Some new results on the number of tagged parts over the partitions with designated summands in which all parts are odd

Authors: Vandna and Mandeep Kaur
Author institution: Department of Mathematics, Lovely Professional University, Phagwara 144 411, Punjab, India.

Summary: Let PDO{t}(n) count the number of tagged parts over the partition function PDO(n), the number of partitions of n with designated summands in which all parts are odd. In this paper, we obtain some new generating functions concerning PDO{t}(n). Also, we establish several new congruences and infinite families of congruences modulo 16, 48, 144, 288, 1152 and 6912 satisfied by PDO{t}(n).

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