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math.CO2026
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}-…
math.CO2026
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…
math.CO2026
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…