Geodesic
On lattices associated with maximal graphical partitions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 32-42
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The aim of this paper is to describe, for a given graphical partition $\lambda$ of weight $2m$ and rank $r$, the set of all maximal graphical partitions $\mu$ of weight $2m$ that dominate $\lambda$. To do this, it is enough to find the set of heads of such partitions. Theorem 1 states that, for any natural number $t$, the set of heads of all maximal graphical partitions $\mu$ of weight $2m$ and rank $t$ dominating $\lambda$ forms an interval of the integer partition lattice if such partitions $\mu$ of rank $t$ exist. Algorithms are also provided for finding the smallest and largest elements of this interval.
Keywords: lattice, Ferrers diagram, graph, maximal graphical partition.
Mots-clés : integer partition 
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V. A. Baranskii; V. V. Zuev. On lattices associated with maximal graphical partitions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 32-42. http://geodesic.mathdoc.fr/item/TIMM_2024_30_1_a2/

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