Analysis and combinatorics of partition zeta functions
Keyword(s):
We examine “partition zeta functions” analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties — those summed over partitions of fixed length — which yields complete information about analytic continuation, poles and trivial roots of the zeta functions in the family. Then we present a combinatorial proof of the explicit formula, which shows it to be a zeta function analog of MacMahon’s partial fraction decomposition of the generating function for partitions of fixed length.
2001 ◽
Vol 71
(1)
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pp. 113-121
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Keyword(s):
2007 ◽
Vol 47
(1)
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pp. 32-47
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Keyword(s):
Keyword(s):
2009 ◽
Vol 61
(6)
◽
pp. 1341-1356
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Keyword(s):
Keyword(s):