15 citations · 29 across the 11 of their papers we have counts for
12 papers
Conguences for Odd Unimodal Sequences and a Problem of Bringmann And Lovejoy
Koustav Banerjee, Manosij Ghosh Dastidar
In this paper, we give a family of the arithmetic progressions in which the numbers of odd unimodal and odd strongly unimodal sequences are divisible by 2 and by 4. In particular,…
The Partition Pairing Theorems I
George Andrews, Manosij Ghosh Dastidar
The aim of this paper is to introduce pairing theory for partitions. We begin with two statistics on integer partitions, the \emph{pairing index} and the \emph{pairing rank}. The p…
Sign Laws and Mock Theta Functions
Manosij Ghosh Dastidar
Let \[ ρ(q)=\sum_{m\geq 0}\frac{q^{2m(m+1)}}{(1+q+q^2)(1+q^3+q^6)\cdots(1+q^{2m+1}+q^{4m+2})} =\sum_{n\geq 0}r(n)q^n \] be Ramanujan's third order mock theta function. We prove the…
Sign law for Ramanujan's third order mock theta function
Manosij Ghosh Dastidar
We study the coefficients of Ramanujan's third order mock theta function \[ ρ(q)=\sum_{m\geq 0} \frac{q^{2m(m+1)}}{(1+q+q^2)(1+q^3+q^6)\cdots(1+q^{2m+1}+q^{4m+2})} =\sum_{n\geq 0}r…
Bijections between Variants of Dyck Paths and Integer Compositions
Manosij Ghosh Dastidar, Michael Wallner
We give bijective results between several variants of lattice paths of length (or ) and integer compositions of n, all enumerated by the seemingly innocuous formula $4^{…
Asymptotics of relaxed -ary trees
Manosij Ghosh Dastidar, Michael Wallner
A relaxed -ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree . These objects arise in the compression of trees in…
Parity biases in partitions and restricted partitions
Koustav Banerjee, Sreerupa Bhattacharjee, Manosij Ghosh Dastidar +2
Let (resp. ) denote the number of partitions of with more odd parts (resp. even parts) than even parts (resp. odd parts). Recently, Kim, Kim, and Lovejoy p…
Some congruences modulo 5 and 25 for overpartition
Shane Chern, Manosij Ghosh Dastidar
We present two new Ramanujan-type congruences modulo 5 for overpartition. We also give an affirmative answer to a conjecture of Dou and Lin, which includes four congruences modulo…
Some results on the cubic partition
Prabir Das Adhikary, Koustav Banerjee, Manosij Ghosh Dastidar
In this paper we explore Kruyswijk's method and show how to obtain congruences for cubic partition. That apart we also examine inequalities for a(n) and provide upper bound for it…
Congruences and recursions for the cubic partition
Shane Chern, Manosij Ghosh Dastidar
Let denote the number of cubic partitions. In this paper, we shall present two new congruences modulo for . We also provide an elementary alternative proof of…
Generalization of a few results in Integer Partitions
Manosij Ghosh Dastidar, Sourav Sen Gupta
In this paper, we generalize a few important results in Integer Partitions; namely the results known as Stanley's theorem and Elder's theorem, and the congruence results proposed b…
Extension of Stanley's Theorem for Partitions
Manosij Ghosh Dastidar, Sourav Sen Gupta
In this paper we present an extension of Stanley's theorem related to partitions of positive integers. Stanley's theorem states a relation between "the sum of the numbers of distin…