2 citations · 3 across the 8 of their papers we have counts for
9 papers
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.
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…
A Complete List of all Numbers not of the Form
Damanvir Singh Binner
For given coprime positive integers and , the classical Frobenius coin problem asked to find the largest number that cannot be expressed in the form for nonnegative…
Reciprocity Relations for Summations of Squares of Floor Functions and Fractional Parts of Fractions
Damanvir Singh Binner
Given positive coprime integers and and a natural number , we obtain reciprocity relations which can be used to quickly evaluate summations like $\sum_{i=1}^{h} \{\frac{…