6 papers
On Partitions with Constant-Sum Gap Sequences
Halime Ömrüuzun Seyrek
We introduce and study \emph{constant-sum gap partitions}: for a fixed nonnegative integer , these are partitions whose successive differences $d_i=λ_{i+1}-…
Part Size Count in Cylindric Partitions and Bijections for Small Profiles
Kağan Kurşungöz, Halime Ömrüuzun Seyrek
We first study the part size statistic in cylindric partitions, listing some specializations of a crude but general formula. Then, we establish bijections between ordinary partitio…
On Partitions with Palindromic Gap Sequences
Halime Ömrüuzun Seyrek
We introduce and study palindromic-gap partitions: partitions whose sequence of successive differences between consecutive parts is a palindrome. We derive the generating function…
A Decomposition of Cylindric Partitions and Cylindric Partitions into Distinct Parts
Kağan Kurşungöz, Halime Ömrüuzun Seyrek
We show that cylindric partitions are in one-to-one correspondence with a pair which has an ordinary partition and a colored partition into distinct parts. Then, we show the genera…
Combinatorial constructions of generating functions of cylindric partitions with small profiles into unrestricted or distinct parts
Kağan Kurşungöz, Halime Ömrüuzun Seyrek
In this paper, cylindric partitions into profiles and are considered. The generating functions into unrestricted cylindric partitions and cylindric partitions i…
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…