10 papers · 1 filter
Sign Patterns in a Two Colored Partition Companion series
Aritram Dhar, Ankush Goswami, Mohit Tripathi
We study two closely related questions arising from the recent work of Andrews and El Bachraoui on the two-color partition series \[ S_1(q)=\sum_{n\ge0}s_1(n)q^n=\sum_{a\ge0}q^a(-q…
Separable integer partition classes and Slater's list -- II
Aritram Dhar, Ankush Goswami, Runqiao Li
Slater's list of Rogers-Ramanujan type identities remains a central source of striking series-product formulas in the theory of partitions and basic hypergeometric series. Although…
Weighted partitions with interval restrictions: exact formulas and a bivariate master identity
George E. Andrews, Mohamed El Bachraoui, Aritram Dhar +2
Let and be the signed partition functions introduced by Andrews and El Bachraoui for interval-restricted partitions whose parts greater than are controlle…
Further Applications of Cubic -Binomial Transformations
Alexander Berkovich, Aritram Dhar
Consider \begin{align*} G(N,M;α,β,K,q) = \sum\limits_{j\in\mathbb{Z}}(-1)^jq^{\frac{1}{2}Kj((α+β)j+α-β)}\left[\begin{matrix}M+N\\N-Kj\end{matrix}\right]_{q}. \end{align*} In…
Separable integer partition classes and Slater's list -- I
Aritram Dhar, Ankush Goswami, Runqiao Li
Slater's list of Rogers-Ramanujan type identities consists of 130 series-product identities whose analytic proofs rely primarily on Bailey pair techniques. Although these identitie…
Inequalities for the number of -hooks in two partition classes arising from sum-product identities
Aritram Dhar, Byungchan Kim, Eunmi Kim +1
Motivated by recent study on the number of -hooks in partitions arising from Euler's partition identity, we investigate the number of -hooks in the sets from the first Rogers…