Automated Generation of Generating Functions Enumerating Families of Core Partitions

By Anthony Zaleski and Doron Zeilberger

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Written: Nov. x 2017


Abstract: Tewodros Amdeberhan and Armin Straub initiated the study of subfamilies of the set of (s,t) core partitions. While the enumeration of (n+1,n+2)-core partitions into distinct parts is relatively easy, the enumeration of (n+1,n+2)-core partitions into odd parts remains elusive. Straub computed the first eleven terms of that sequence, (see penultimate slide of Armin Straub's talk), and asked for a "formula", or at least a fast way to compute many terms. While we are unable to find a `fast' algorithm, we did manage to find a `faster' algorithm, that enabled us to compute 23 terms of this intriguing sequence. We strongly believe that this sequence has an algebraic generating function, since a `sister sequnece' (see the article), is OEIS sequence A047749 that does have an algebraic generating function. We also develop algorithms, and find explicit generating functions, for other families of (n+1,n+2)-core partitions.


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Sample Input and Output for OddArmin.txt


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