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math.CO2021★ 1 cited
Stanley--Elder--Fine theorems for colored partitions
Hartosh Singh Bal, Gaurav Bhatnagar
We give a new proof of a partition theorem popularly known as Elder's theorem, but which is also credited to Stanley and Fine. We extend the theorem to the context of colored parti…
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…