On k-partitions of multisets with equal sums

Abstract We study the number of ordered k -partitions a multiset with equal sums, having elements $$\alpha _1,\ldots ,\alpha _n$$ α 1 , … n and multiplicities $$m_1,\ldots ,m_n$$ m . Denoting this by $$S_k(\alpha _1, \ldots , \alpha _n; m_1, m_n)$$ S k ( ; ) we find generating function, derive an integral formula, illustrate results numerical examples. The special case involving set $$\{1,\dots ,n\}$$ { ⋯ } presents particular interest leads to new integer sequences $$S_k(n)$$ $$Q_k(n)$$ Q $$R_k(n)$$ R for which provide explicit formulae combinatorial interpretations. Conjectures in connection some superelliptic Diophantine equations asymptotic formula are also discussed. extend previous work concerning 2- 3-partitions multisets.