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On the Dimension of Downsets of Integer Partitions and Compositions by Engen, Michael; Vatter, Vincent is a scholarly article available to read on EtoBox.

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We characterize the downsets of integer partitions (ordered by containment of Ferrers diagrams) and compositions (ordered by the generalized subword order) which have finite dimension in the sense of Dushnik and Miller. In the case of partitions, while the set of all partitions has infinite dimension, we show that every proper downset of partitions has finite dimension. For compositions we identify four minimal downsets of infinite dimension and establish that every downset which does not contain one of these four has finite dimension.

Author

Engen, Michael; Vatter, Vincent

Published

2017

Language

EN