When does the set of \((a, b, c)\)-core partitions have a unique maximal element?
The electronic journal of combinatorics, Tome 22 (2015) no. 2
In 2007, Olsson and Stanton gave an explicit form for the largest $(a, b)$-core partition, for any relatively prime positive integers $a$ and $b$, and asked whether there exists an $(a, b)$-core that contains all other $(a, b)$-cores as subpartitions; this question was answered in the affirmative first by Vandehey and later by Fayers independently. In this paper we investigate a generalization of this question, which was originally posed by Fayers: for what triples of positive integers $(a, b, c)$ does there exist an $(a, b, c)$-core that contains all other $(a, b, c)$-cores as subpartitions? We completely answer this question when $a$, $b$, and $c$ are pairwise relatively prime; we then use this to generalize the result of Olsson and Stanton.
DOI :
10.37236/4773
Classification :
05A17
Mots-clés : Young diagram, hook length, core partition, numerical semigroup, UM-set, poset-UM
Mots-clés : Young diagram, hook length, core partition, numerical semigroup, UM-set, poset-UM
Affiliations des auteurs :
Amol Aggarwal 1
@article{10_37236_4773,
author = {Amol Aggarwal},
title = {When does the set of \((a, b, c)\)-core partitions have a unique maximal element?},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/4773},
zbl = {1325.05024},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4773/}
}
Amol Aggarwal. When does the set of \((a, b, c)\)-core partitions have a unique maximal element?. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4773
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