Reductions of additive sets, sets of uniqueness and pyramids
type: Item
instance of: scholarly article
title: Reductions of additive sets, sets of uniqueness and pyramids
zbMATH Open document ID: 0901.05008
DOI: 10.1016/S0012-365X(96)00134-3
author: Ernesto Vallejo
published in: Discrete Mathematics
publication date: 1998-11-22T00:00:00Z
review text: If \([m]= \{1,\dots, m\}\), \(m\) a positive integer, consider the three-dimensional box \(B= [p]\times [q]\times [r]\), with \(S\) a subset of \(B\). The idea of a reduction of a set is introduced and an equivalence relation is defined on \(B\). Two subsets of \(B\) are box equivalent if both can be reduced to a third set; every set in this class can be reduced to it. A set \(S\) in \(B\) is additive if and only if any reduction of \(S\) is additive. A special class of subsets called pyramids is introduced and it is pointed out that there is a one-to-one correspondence between these and plane partitions, already known to P. A. MacMahon.
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 1062452
zbMATH Keywords: pyramids
zbMATH Keywords: plane partitions
reviewed by: Gerald L. Alexanderson
MaRDI profile type: Publication
cites work: Q3050437
cites work: Sets uniquely determined by projections on axes. II: Discrete case
cites work: Symmetries of plane partitions
cites work: The enumeration of totally symmetric plane partitions
description: scientific article; zbMATH DE number 1062452