2 citations · 5 across the 13 of their papers we have counts for
13 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.
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…
Proofs of Chappelon and Alfons\'ın Conjectures On Square Frobenius Numbers and its Relationship to Simultaneous Pell's Equations
Damanvir Singh Binner
Recently, Chappelon and Alfons\'ın defined the square Frobenius number of coprime numbers and to be the largest perfect square that cannot be expressed in the form …
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{…
Some Bounds for Number of Solutions to and their Applications
Damanvir Singh Binner
In a recent work, the present author developed an efficient method to find the number of solutions of in non-negative integer triples where and a…
Generalization of a Result of Sylvester Regarding the Frobenius Coin Problem and an Elementary Proof of Eisenstein's Lemma for Jacobi Symbols
Damanvir Singh Binner
In a recent work, the present author generalized a fundamental result of Gauss related to quadratic reciprocity, and also showed that the above result of Gauss is equivalent to a s…
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…
Number of Non-negative Integer Solutions of the Equation ax+by+cz=n and its Relation with Quadratic Residues
Damanvir Singh Binner
In 2000, A. Tripathi used generating functions to obtain a formula for the number of non-negative solutions (x,y) of the equation ax + by = n where a, b and n are given positive in…