7 papers
An Alternative Generating Function for -Regular Partitions
Kağan Kurşungöz
We construct a -fold -series as a generating function of -regular partitions for each positive integer . The case is one of Euler's -series identities pertaini…
Modulo extension of parity results in Rogers-Ramanujan-Gordon type overpartition identities
Kağan Kurşungöz, Mohammad Zadehdabbagh
Sang, Shi and Yee, in 2020, found overpartition analogs of Andrews' results involving parity in Rogers-Ramanujan-Gordon identities. Their result partially answered an open question…
Construction of Evidently Positive Series and An Alternative Construction for a Family of Partition Generating Functions due to Kanade and Russell
Kağan Kurşungöz, Halime Ömrüuzun Seyrek
We give an alternative construction for a family of partition generating functions due to Kanade and Russell. In our alternative construction, we use ordinary partitions instead of…
A combinatorial construction for two formulas in Slater's List
Kağan Kurşungöz
We set up a combinatorial framework for inclusion-exclusion on the partitions into distinct parts to obtain an alternative generating function of partitions into distinct and non-c…
Andrews-Gordon Type Series for Schur's Partition Identity
Kağan Kurşungöz
We construct an evidently positive multiple series as a generating function for partitions satisfying the multiplicity condition in Schur's partition theorem. Refinements of the se…
Andrews-Gordon Type Series for Kanade-Russell Conjectures
Kağan Kurşungöz
We construct Andrews-Gordon type evidently positive series as generating functions of partitions satisfying certain difference conditions in six conjectures by Kanade and Russell.…