6 papers
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 [\…
Hook Length Biases in -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…
Combinatorial proofs of some identities on overpartitions with repeated smallest non-overlined part
Nayandeep Deka Baruah, Haijun Li, Pankaj Jyoti Mahanta
Let denote the number of overpartitions of where the smallest non-overlined part, say , appears times and every overlined part is bigge…
Biases in Non-Unitary Partitions
Pankaj Jyoti Mahanta, Manjil P. Saikia, Abhishek Sarma
Recently, the concept of parity bias in integer partitions has been studied by several authors. We continue this study here, but for non-unitary partitions (namely, partitions with…
On hook length biases in -regular partitions
Rupam Barman, Pankaj Jyoti Mahanta, Gurinder Singh
Let and be integers. A -regular partition of a positive integer is a partition of such that none of its parts is divisible by . Let den…
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 -series identities, from which three simple looking identities involving certain restricted partitions in…