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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 -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 denote the number of overpartitions of where the smallest non-overlined part, say , appears times and every overlined part is bigger…