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math.NT2021
Glaisher's divisors and infinite products
Hartosh Singh Bal, Gaurav Bhatnagar
Ramanujan gave a recurrence relation for the partition function in terms of the sum of the divisor function . In 1885, J.W. Glaisher considered seven divisor sums closely rel…
math.NT2021★ 4 cited
The Partition-Frequency Enumeration Matrix
Hartosh Singh Bal, Gaurav Bhatnagar
We develop a calculus that gives an elementary approach to enumerate partition-like objects using an infinite upper-triangular number-theoretic matrix. We call this matrix the Part…