21 citations · 23 across the 6 of their papers we have counts for
8 papers · 1 filter
On Finite Analogs of Schmidt's Problem and Its Variants
Alexander Berkovich, Ali Kemal Uncu
We refine Schmidt's problem and a partition identity related to 2-color partitions which we will refer to as Uncu-Andrews-Paule theorem. We will approach the problem using Boulet-S…
Weighted cylindric partitions
Walter Bridges, Ali Uncu
Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a the…
Cylindric partitions and some new Rogers-Ramanujan identities
Sylvie Corteel, Jehanne Dousse, Ali K. Uncu
We study the generating functions for cylindric partitions with profile for all such that . This allows us to discover and prove seven…
On a weighted spin of the Lebesgue Identity
Ali K. Uncu
Alladi studied partition theoretic implications of a two variable generalization of the Lebesgue identity. In this short note, we focus on a slight variation of the basic hypergeom…
A Polynomial Identity Implying Schur's Partition Theorem
Ali K. Uncu
We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kurşungöz.…
Some Elementary Partition Inequalities and Their Implications
Alexander Berkovich, Ali K. Uncu
We prove various inequalities between the number of partitions with the bound on the largest part and some restrictions on occurrences of parts. We explore many interesting consequ…