9 papers · 1 filter
Combinatorial construction of known positive series for partition classes defined by Capparelli, Meurman, Primc, and Primc in the =1 Case
Kağan Kurşungöz
Recently, Capparelli, Meurman, A. Primc and M. Primc introduced a class of colored partitions which has since been called CMPP partitions. This generalized earlier work by M. Primc…
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.…
Bressoud Style Identities for Regular Partitions and Overpartitions
Kağan Kurşungöz
We construct a family of partition identities which contain the following identities: Rogers-Ramanujan-Gordon identities, Bressoud's even moduli generalization of them, and their c…
Andrews Style Partition Identities
Kağan Kurşungöz
We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is…