Geodesic
On maximal graphical partitions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 112-124

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A partition of an integer $m$ is a sequence of nonnegative integers in nonincreasing order whose sum is equal to $m$. The length of a partition is the number of its nonzero parts. The set of all graphical partitions of $2m$, for a given $m$, is an order ideal of the lattice of all partitions of $2m$. We find new characterization of maximal graphical partitions and the number of maximal graphical partitions of length $n$. For each graphical partition $\lambda$ of integer $2m$ we construct maximal graphical partition $\mu$ of integer $2m$ with the same rank, which is dominate $\lambda$; also we find an algorithm that builds a sequence of elementary transformations from $\mu$ to $\lambda$.
Keywords: graph, lattice, graphical partition, Ferrer's diagram.
Mots-clés : integer partition 
@article{SEMR_2017_14_a3,
     author = {V. A. Baransky and T. A. Senchonok},
     title = {On maximal graphical partitions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {112--124},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a3/}
}
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V. A. Baransky; T. A. Senchonok. On maximal graphical partitions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 112-124. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a3/