2008/09/12 by Joseph Vandehey, Vandehey, Joseph · 1 citation
Computer Science · Mathematics · #05A17 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:05A17
paper · pdf · doi:10.48550/arxiv.0809.2134
75 pages, originally an undergraduate thesis titled "A Complete Theory of (s,t)-core Partitions"
arxiv created 2008/09/12 · openalex publication_date 2008/09/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the idea of (s,t)-closure and delta-sets and show that (s,t)-closed beta-sets which are contained set-wise in (s,t)-closed delta-sets are also contained partition-wise. This implies the maximal (s,t)-core partition theorem of Olsson and Stanton. Along the way, we reprove the (s,s+1)-core case, originally proved by Olsson and Stanton, using new techniques, and several lemmas and propositions regarding the containment of partitions are presented as well. Finally, we study how these apply to partitions which are T-core.