P. Mahanta

activity

20202026

most citedParity biases in partitions and restricted partitions

10 citations · 21 across the 14 of their papers we have counts for

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12 papers · 1 filter

math.CO2026

A Proof of a Conjecture on Fixed Perimeter Partitions

Pankaj Jyoti Mahanta

Finding fixed perimeter analogues of various partition theoretic identities and inequalities has recently emerged as an active area of research. Gray, Payne, Swisher, and Watson [\…

math.CO2026

Hook Length Biases in $t$ -Core Partitions

Nayandeep Deka Baruah, Hirakjyoti Das, Pankaj Jyoti Mahanta +1

Recently, the theory of hook length biases has emerged as a prominent research topic. Led by Ballantine, Burson, Craig, Folsom, and Wen [\textit{Res. Math. Sci.}, 2023], hook lengt…

math.CO2026

Combinatorial proofs of some identities on overpartitions with repeated smallest non-overlined part

Nayandeep Deka Baruah, Haijun Li, Pankaj Jyoti Mahanta

Let $spt k (n)$ denote the number of overpartitions of $n$ where the smallest non-overlined part, say $s (π)$ , appears $k$ times and every overlined part is bigger…

math.CO2025

On hook length biases in $t$ -regular partitions

Rupam Barman, Pankaj Jyoti Mahanta, Gurinder Singh

Let $t \geq 2$ and $k \geq 1$ be integers. A $t$ -regular partition of a positive integer $n$ is a partition of $n$ such that none of its parts is divisible by $t$ . Let $b_{t, k} (n)$ den…

math.CO2024

Combinatorial Proofs of Some Results of Andrews and El Bachraoui

Pankaj Jyoti Mahanta, Manjil P. Saikia

Recently, Andrews and El Bachraoui (2024) proved three very interesting $q$ -series identities, from which three simple looking identities involving certain restricted partitions in…

math.CO2023

Extensions of some results of Jovovic and Dhar

Pankaj Jyoti Mahanta, Manjil P. Saikia

We look at extensions of formulas given by Jovovic and recently proved by Dhar on integer partitions where the smallest part occurs at least $m$ times and on integer partitions wit…

math.CO2021★ 3 cited

Refinement of some partition identities of Merca and Yee

Pankaj Jyoti Mahanta, Manjil P. Saikia

Recently, Merca and Yee proved some partition identities involving two new partition statistics. We refine these statistics and generalize the results of Merca and Yee. We also cor…

math.CO2021★ 10 cited

Parity biases in partitions and restricted partitions

Koustav Banerjee, Sreerupa Bhattacharjee, Manosij Ghosh Dastidar +2

Let $p_{o} (n)$ (resp. $p_{e} (n)$ ) denote the number of partitions of $n$ with more odd parts (resp. even parts) than even parts (resp. odd parts). Recently, Kim, Kim, and Lovejoy p…

math.CO2021

Partial sums of the Gibonacci sequence

Pankaj Jyoti Mahanta

Recently, Chu studied some properties of the partial sums of the sequence $P^{k} (F_{n})$ , where $P (F_{n}) = (\sum_{i = 1}^{n} F_{i})_{n \geq 1}$ and $(F_{n})_{n \geq 1}$ is the Fibonacci sequen…

math.CO2020

On the number of partitions of $n$ whose product of the summands is at most $n$

Pankaj Jyoti Mahanta

We prove an explicit formula to count the partitions of $n$ whose product of the summands is at most $n$ . In the process, we also deduce a result to count the multiplicative partit…

math.CO2020

Some New and Old Gibonacci Identities

Pankaj Jyoti Mahanta, Manjil P. Saikia

We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several…

math.CO2020★ 1 cited

A family of lacunary recurrences for Lucas Numbers

Pankaj Jyoti Mahanta, Manjil P. Saikia

We prove an infinite family of lacunary recurrences for the Lucas numbers using combinatorial means.

A Proof of a Conjecture on Fixed Perimeter Partitions

Hook Length Biases in t-Core Partitions

Combinatorial proofs of some identities on overpartitions with repeated smallest non-overlined part

On hook length biases in t-regular partitions

Combinatorial Proofs of Some Results of Andrews and El Bachraoui

Extensions of some results of Jovovic and Dhar

Refinement of some partition identities of Merca and Yee

Parity biases in partitions and restricted partitions

Partial sums of the Gibonacci sequence

On the number of partitions of n whose product of the summands is at most n

Some New and Old Gibonacci Identities

A family of lacunary recurrences for Lucas Numbers

Hook Length Biases in $t$ -Core Partitions

On hook length biases in $t$ -regular partitions

On the number of partitions of $n$ whose product of the summands is at most $n$