2 citations · 5 across the 13 of their papers we have counts for
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On conjectures of Chern concerning parity bias in partitions
Damanvir Singh Binner
We prove recent conjectures of Chern concerning nonnegativity of a certain q-series related to parity bias in integer partitions.
On -measures and Durfee squares of partitions
Damanvir Singh Binner
Recently, Andrews, Bhattacharjee and Dastidar introduced the concept of -measure of an integer partition, and proved a surprising identity that the number of partitions of w…
A Comparison of Integer Partitions Based on Smallest Part
Damanvir Singh Binner, Amarpreet Rattan
For positive integers and , consider the following two sets that both contain partitions of with the difference between the largest and smallest parts bounded by :…
Number of partitions of n into parts not divisible by m
Damanvir Singh Binner
In this note, we obtain a formula which leads to a practical and efficient method to calculate the number of partitions of n into parts not divisible by m for given natural numbers…
Number of partitions of n with a given parity of the smallest part
Damanvir Singh Binner
We obtain a combinatorial proof of a surprising weighted partition equality of Berkovich and Uncu. Our proof naturally leads to a formula for the number of partitions with a given…
Berkovich-Uncu type Partition Inequalities Concerning Impermissible Sets and Perfect Power Frequencies
Damanvir Singh Binner, Neha Gupta, Manoj Upreti
Recently, Rattan and the first author (Ann. Comb. 25 (2021) 697-728) proved a conjectured inequality of Berkovich and Uncu (Ann. Comb. 23 (2019) 263-284) concerning partitions with…
On Conjectures Concerning the Smallest Part and Missing Parts of Integer Partitions
Damanvir Singh Binner, Amarpreet Rattan
For positive integers and , Berkovich and Uncu (Ann. Comb. () --) conjectured an inequality between the sizes of two closely related sets of part…