From the 1 of 10 linked papers with an AI index.
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-generalization of the Rogers-Ramanujan-Gordon identities via commutative algebra
Alapan Ghosh, Rupam Barman
The Rogers-Ramanujan-Gordon identities generalize the classical partition identities discovered independently by L. J. Rogers and S. Ramanujan. In 2021, Afsharijoo provided a commu…
On the Göllnitz-Gordon-Andrews identities via commutative algebra
Rupam Barman, Alapan Ghosh, Gurinder Singh
The Göllnitz-Gordon-Andrews identities generalize the classical partition identities discovered independently by H. Göllnitz and B. Gordon. These are Rogers-Ramanujan-type identi…
Hook length inequalities for -regular partitions in the -aspect
Gurinder Singh, Rupam Barman
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…
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…
Hook length biases in ordinary and -regular partitions
Gurinder Singh, Rupam Barman
In this article, we study hook lengths of ordinary partitions and -regular partitions. We establish hook length biases for the ordinary partitions and motivated by them we find…