Partition theorems for Euler pairs
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- by M. V. Subbarao PDF
- Proc. Amer. Math. Soc. 28 (1971), 330-336 Request permission
Abstract:
This paper generalizes and extends the recent results of George Andrews on Euler pairs. If ${S_1}$ and ${S_2}$ are nonempty sets of natural numbers, we define $({S_1},{S_2})$ to be an Euler pair of order $r$ whenever ${q_r}({S_1};n) = p({S_2};n)$ for all natural numbers $n$, where ${q_r}({S_1};n)$ denotes the number of partitions of $n$ into parts taken from ${S_1}$, no part repeated more than $r - 1$ times $(r > 1)$, and $p({S_2};n)$ the number of partitions of $n$ into parts taken from ${S_2}$. Using a method different from Andrews’, we characterize all such pairs, and consider various applications as well as an extension to vector partitions.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 330-336
- MSC: Primary 10.48
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274410-1
- MathSciNet review: 0274410