Many links exist between ordinary partitions and partitions with parts in the “gaps”. In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then .
@article{bwmeta1.element.bwnjournal-article-aav85i2p119bwm,
author = {Dennis Eichhorn},
title = {A combinatorial approach to partitions with parts in the gaps},
journal = {Acta Arithmetica},
volume = {84},
year = {1998},
pages = {119-133},
zbl = {0930.11074},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav85i2p119bwm}
}
Dennis Eichhorn. A combinatorial approach to partitions with parts in the gaps. Acta Arithmetica, Tome 84 (1998) pp. 119-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav85i2p119bwm/
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