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Autor:
Singh, Gurinder, Barman, Rupam
Let $t\geq2$ and $k\geq1$ 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 $t$. A $t$-distinct partition of a positive integer $n$ is a partition of $n$ such that any of
Externí odkaz:
http://arxiv.org/abs/2410.15088
Autor:
Singh, Gurinder, Barman, Rupam
In this article, we study hook lengths of ordinary partitions and $t$-regular partitions. We establish hook length biases for the ordinary partitions and motivated by them we find a few interesting hook length biases in $2$-regular partitions. For a
Externí odkaz:
http://arxiv.org/abs/2404.07485
Autor:
Singh, Gurinder, Barman, Rupam
The minimal excludant of an integer partition is the least positive integer missing from the partition. Let $\sigma_o\text{mex}(n)$ (resp., $\sigma_e\text{mex}(n)$) denote the sum of odd (resp., even) minimal excludants over all the partitions of $n$
Externí odkaz:
http://arxiv.org/abs/2310.20628
Autor:
Singh, Gurinder, Barman, Rupam
Lin introduced the partition function $\text{PDO}_t(n)$, which counts the total number of tagged parts over all the partitions of $n$ with designated summands in which all parts are odd. For $k\geq0$, Lin conjectured congruences for $\text{PDO}_t(8\c
Externí odkaz:
http://arxiv.org/abs/2307.04687
Publikováno v:
Asia Pacific Journal of Marketing and Logistics, 2024, Vol. 36, Issue 7, pp. 1634-1656.
Externí odkaz:
http://www.emeraldinsight.com/doi/10.1108/APJML-07-2023-0690
For a positive integer $t\geq 2$, let $b_{t}(n)$ denote the number of $t$-regular partitions of a nonnegative integer $n$. In a recent paper, Keith and Zanello investigated the parity of $b_{t}(n)$ when $t\leq 28$. They discovered new infinite famili
Externí odkaz:
http://arxiv.org/abs/2301.11192