1 citations · 3 across the 4 of their papers we have counts for
5 papers
A Family of Congruences Modulo 7 for Partitions with Monochromatic Even Parts and Multi--Colored Odd Parts
Michael D. Hirschhorn, James A. Sellers
In recent work, Amdeberhan and Merca considered the integer partition function which counts the number of integer partitions of weight wherein even parts come in only on…
Elementary Proofs of Infinitely Many Congruences for -Elongated Partition Diamonds
Robson da Silva, Michael D. Hirschhorn, James A. Sellers
In 2007, Andrews and Paule published the eleventh paper in their series on MacMahon's partition analysis, with a particular focus on broken -diamond partitions. On the way to br…
A formula for the convergents of a continued fraction of Ramanujan
Gaurav Bhatnagar, Michael D. Hirschhorn
In Entry 16, Chapter 16 of his notebooks, Ramanujan himself gave a formula for the convergents of the famous Rogers-Ramanujan continued fraction. We provide a similar formula for t…
Arithmetic Properties of Andrews' Singular Overpartitions
Shi-Chao Chen, Michael D. Hirschhorn, James A. Sellers
In a very recent work, G. E. Andrews defined the combinatorial objects which he called {\it singular overpartitions} with the goal of presenting a general theorem for overpartition…
A Refinement of Ramanujan's Factorial Approximation
Michael D. Hirschhorn, Mark B. Villarino
We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function