Johnson's bijections and their application to counting simultaneous core partitions

Jineon Baek, Hayan Nam, Myungjun Yu

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Johnson recently proved Armstrong's conjecture which states that the average size of an (a,b)-core partition is (a+b+1)(a−1)(b−1)∕24. He used various coordinate changes and one-to-one correspondences that are useful for counting problems about simultaneous core partitions. We give an expression for the number of (b1,b2,…,bn)-core partitions where {b1,b2,…,bn} contains at least one pair of relatively prime numbers. We also evaluate the largest size of a self-conjugate (s,s+1,s+2)-core partition.

Original languageEnglish
Pages (from-to)43-54
Number of pages12
JournalEuropean Journal of Combinatorics
Publication statusPublished - 2019 Jan

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Ltd

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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