14 papers
Extending Recent Arithmetic Properties of Overcubic Partition Tuples
Saikat Maity, Manjil P. Saikia
In recent years, several mathematicians have looked at a class of partitions called the overcubic partition -tuples, for small values of . They have proved several divisibili…
Some Comments on Regular Overpartitions modulo
Abdulaziz M. Alanazi, Manjil P. Saikia
For coprime integers , Alanazi, Munagi, and Saikia (2026) studied , the number of overpartitions of in which no part is divisible by $\…
Dyck paths on colored lattices
Manjil P. Saikia
Fried recently enumerated Dyck paths having equally many black and white cells below them, for the chessboard coloring (Narayana numbers) and the column-alternating coloring (Fuss-…
QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs
Santiago Gonzalez, Alireza Amiri Bavandpour, Peter Ye +48
As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that st…
New arithmetic properties for overpartitions where nonoverlined parts are -regular
Hemjyoti Nath, Manjil P. Saikia, James A. Sellers
In this paper, we study the partition functions , which count the number of overpartitions of where the non-overlined parts are -regular for a…
Arithmetic Properties of Generalized Cubic and Overcubic Partitions
Hirakjyoti Das, Saikat Maity, Manjil P. Saikia
We prove several congruences satisfied by the generalized cubic and generalized overcubic partition functions, recently introduced by Amdeberhan, Sellers, and Singh. We also prove…