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A combinatorial approach to partitions with parts in the gaps

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Eichhorn D.

Acta Arithmetica

1998

tom 85

nr 2

119-133

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 $p^_{k,m}(j,n)$ be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let $p*_{k,m}(j,n)$ 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 $p*_{k,m}(j,n)=p_{k,m}(j,n)$.

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1 Acta Arithmetica

1 Eichhorn D.

1 1998

Wyniki wyszukiwania

A combinatorial approach to partitions with parts in the gaps