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- Title
Minimal Partitions with a Given s-Core and t-Core.
- Authors
Fayers, Matthew
- Abstract
Suppose s and t are coprime positive integers, and let σ be an s-core partition and τ a t-core partition. In this paper, we consider the set P σ , τ (n) of partitions of n with s-core σ and t-core τ . We find the smallest n for which this set is non-empty, and show that for this value of n the partitions in P σ , τ (n) (which we call (σ , τ) -minimal partitions) are in bijection with a certain class of (0, 1)-matrices with s rows and t columns. We then use these results in considering conjugate partitions: we determine exactly when the set P σ , τ (n) consists of a conjugate pair of partitions, and when P σ , τ (n) contains a unique self-conjugate partition.
- Subjects
INTEGERS; PARTITIONS (Mathematics)
- Publication
Annals of Combinatorics, 2023, Vol 27, Issue 2, p297
- ISSN
0218-0006
- Publication type
Article
- DOI
10.1007/s00026-022-00577-4