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Another smallest part function related to Andrews' spt function

100%
Patkowski A.
Acta Arithmetica
|
2015
|
tom 168
|
nr 2
101-105
EN
We offer some relations and congruences for two interesting spt-type functions, which together form a relation to Andrews' spt function.
2
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On Some Partition Functions Related to Some Mock Theta Functions

100%
Patkowski A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom 57
|
nr 1
1-8
EN
We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.
3
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Divisors, partitions and some new q-series identities

100%
Patkowski A.
Colloquium Mathematicum
|
2009
|
tom 117
|
nr 2
289-294
EN
We obtain new q-series identities that have interesting interpretations in terms of divisors and partitions. We present a proof of a theorem of Z. B. Wang, R. Fokkink, and W. Fokkink, which follows as a corollary to our main q-series identity, and offer a similar result.
4
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On Bailey pairs and certain q-series related to quadratic and ternary quadratic forms

100%
Patkowski A.
Colloquium Mathematicum
|
2011
|
tom 122
|
nr 2
265-273
EN
We provide a new approach to establishing certain q-series identities that were proved by Andrews, and show how to prove further identities using conjugate Bailey pairs. Some relations between some q-series and ternary quadratic forms are established.
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