2 citations · 2 across the 16 of their papers we have counts for
6 papers · 2 filters
Versions of Andrews-Gordon Identities Revisited
Alexander Berkovich, Aritram Dhar
In this paper, we revisit the work of Berkovich and Paule on variants of the Andrews-Gordon identities. We find a generalization of their principal polynomial identity and, as a co…
Sign Patterns in a Two Colored Partition Companion series
Aritram Dhar, Ankush Goswami, Mohit Tripathi
We study three 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(…
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…
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…