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A short note on the weighted sub-partition mean of integers. (English) Zbl 1231.05017
Summary: We study weighted sub-partitions \((i_{1},\dots ,i_l)\) of positive integers on a number \(n\) with the greatest sub-partition mean \(\sum _{k=1}^l w(i_k)/l\), where \(w: \{1,\dots ,n\}\to \mathcal R^+\) is a weight function. We show that this problem is closely related with the problem of computing the eigenvalue of a Toeplitz matrix in a specific form.

MSC:
05A17 Combinatorial aspects of partitions of integers
15A15 Determinants, permanents, traces, other special matrix functions
15A18 Eigenvalues, singular values, and eigenvectors
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