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Embedding a partition in various triangles.
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This article is part of an ongoing investigation of the combinatorics of $q,t$-Catalan numbers $\textrm{Cat}_n(q,t)$. We develop a structure theory for integer partitions based on the partition statistics dinv, deficit, and minimum triangle height. Our goal is to decompose the infinite set of partitions of deficit $k$ into a disjoint union of chain...
Contexts in source publication
Context 1
... λ = 5441. Figure 1 shows the diagrams of λ and ∆ n for n = 5, 6, 7, 8. We have qdv 5 (λ) = 00(−2)(−1)(−1), qdv 6 (λ) = 011(−1)00, qdv 7 (λ) = 0122011, qdv 8 (λ) = 01233122, and min ∆ (λ) = 7. ...
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