Geodesic
Lattices of partial sums
Algebra and discrete mathematics, Tome 18 (2014) no. 2, pp. 171-185

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In this paper we introduce and study a class of partially ordered sets that can be interpreted as partial sums of indeterminate real numbers. An important example of these partially ordered sets, is the classical Young lattice $\mathbb{Y}$ of the integer partitions. In this context, the sum function associated to a specific assignment of real values to the indeterminate variables becomes a valuation on a distributive lattice.
Keywords: distributive lattices, real partial sums
Mots-clés : integer partitions. 
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Giampiero Chiaselotti; Tommaso Gentile; Paolo Antonio Oliverio. Lattices of partial sums. Algebra and discrete mathematics, Tome 18 (2014) no. 2, pp. 171-185. http://geodesic.mathdoc.fr/item/ADM_2014_18_2_a2/