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

Tewodros Amdeberhan and Armin Straub initiated the study of enumeratingsubfamilies of the set of (s,t)-core partitions. While the enumeration of(n+1,n+2)-core partitions into distinct parts is relatively easy (in fact itequals the Fibonacci number F_{n+2}), the enumeration of (n+1,n+2)-corepartitions into odd parts remains elusive.  Straub computed the first eleven terms of that sequence, and asked for a"formula," or at least a fast way, to compute many terms. While we are unableto find a "fast" algorithm, we did manage to find a "faster" algorithm, whichenabled us to compute 23 terms of this intriguing sequence. We strongly believethat this sequence has an algebraic generating function, since a "sistersequence" (see the article), is OEIS sequence A047749 that does have analgebraic generating function. One of us (DZ) is pledging a donation of 100dollars to the OEIS, in honor of the first person to generate sufficiently manyterms to conjecture (and prove non-rigorously) an algebraic equation for thegenerating function of this sequence, and another 100 dollars for a rigorousproof of that conjecture.  Finally, we also develop algorithms that find explicit generating functionsfor other, more tractable, families of (n+1,n+2)-core partitions.

On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts