English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove three main conjectures of Berkovich and Uncu (Ann. Comb. 23 (2019)263--284) on the inequalities between the numbers of partitions of $n$ withbounded gap between largest and smallest parts for sufficiently large $n$.Actually our theorems are stronger than their original conjectures. Theanalytic version of our results shows that the coefficients of some partition$q$-series are eventually positive.

Gap between the largest and smallest parts of partitions and Berkovich and Uncu's conjectures