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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2014, Volume 18, Issue 2, Pages 171–185 (Mi adm490)

RESEARCH ARTICLE

Lattices of partial sums

Giampiero Chiaselotti, Tommaso Gentile, Paolo Antonio Oliverio

Università degli Studi della Calabria, Dipartimento di Matematica

Abstract: 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, integer partitions.

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Bibliographic databases:
MSC: Primary 06A06; Secondary 06A07, 05A17
Revised: 06.06.2013
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Citation: Giampiero Chiaselotti, Tommaso Gentile, Paolo Antonio Oliverio, “Lattices of partial sums”, Algebra Discrete Math., 18:2 (2014), 171–185

Citation in format AMSBIB
\Bibitem{ChiGenOli14} \by Giampiero~Chiaselotti, Tommaso~Gentile, Paolo~Antonio~Oliverio \paper Lattices of partial sums \jour Algebra Discrete Math. \yr 2014 \vol 18 \issue 2 \pages 171--185 \mathnet{http://mi.mathnet.ru/adm490} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3352708} 

1. S. M. Sanahuja, “New rough approximations for $n$-cycles and $n$-paths”, Appl. Math. Comput., 276 (2016), 96–108