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In this paper we define a new class of partially filled arrays, called λ-fold relative Heffter arrays, that are a generalisation of the Heffter arrays introduced by Archdeacon in 2015. After showing the connection of this new concept with several other ones, such as signed magic arrays, graph decompositions and relative difference families, we determine some necessary conditions and we present existence results for infinite classes of these arrays. In the last part of the paper we also showarXiv:2010.10948v1 fatcat:dclss3brzrfzdmz3feivudc3ye