Results 11 to 20 of about 50 (48)
The false theta functions of Rodgers and their modularity
Bulletin of the London Mathematical Society, Volume 53, Issue 4, Page 963-980, August 2021., 2021 Abstract In this survey article, we explain how false theta functions can be embedded into a modular framework and show some of the applications of this modularity.
Kathrin Bringmann
wiley +1 more source
A family of partitions with attached parts and 'N copies of N' [PDF]
, 2015 in this paper we find two distinct combinatorial interpretations for a family of summations with several free parameters. In one case we used partitions with attached parts and in the other partitions with 'N copies of N'.
Mondek, P, Santos, JPO
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New congruences Modulo 5 and 9 for partitions with odd parts distinct [PDF]
, 2021 Let pod(n) denote the number of partitions of an integer n wherein the odd parts are distinct. Recently, a number of congruences for pod(n) have been established.
Xue, Fanggang +2 more
core
On the existence of a non‐zero lower bound for the number of Goldbach partitions of an even integer
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 15, Page 789-798, 2004., 2004 The Goldbach partitions of an even number, given by the sums of two prime addends, form the nonempty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non‐zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4.
Simon Davis
wiley +1 more source
Congruences in ordered pairs of partitions
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 47, Page 2509-2512, 2004., 2004 Dyson defined the rank of a partition (as the first part minus the number of parts) whilst investigating certain congruences in the sequence p−1(n). The rank has been widely studied as have been other statistics, such as the crank. In this paper a “birank” is defined which relates to ordered pairs of partitions, and is used in an elementary proof of a ...
Paul Hammond, Richard Lewis
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Computational proofs of congruences for 2‐colored Frobenius partitions
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 6, Page 333-340, 2002., 2002 In 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2‐colored Frobenius partitions of n: for all n ≥ 0 and α ≥ 1, cΦ2(5αn + λα) ≡ 0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. In this paper, the first four cases of this family are proved.
Dennis Eichhorn, James A. Sellers
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The Kostant partition functions for twisted Kac‐Moody algebras
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 1, Page 11-27, 2000., 2000 Employing the method of generating functions and making use of some infinite product identities like Euler, Jacobi′s triple product and pentagon identities we derive recursion relations for Kostant′s partition functions for the twisted Kac‐Moody algebras.
Ranabir Chakrabarti +1 more
wiley +1 more source
On congruence properties of the partition function
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 7, Page 493-496, 2000., 2000 Some congruence properties of the partition function are proved.
Jayce Getz
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On partitions with difference conditions
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 8, Page 519-527, 2000., 2000 We present two general theorems having interesting special cases. From one of them we give a new proof for theorems of Gordon using a bijection and from another we have a new combinatorial interpretation associated with a theorem of Göllnitz.
José Plínio, O. Santos, Paulo Mondek
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q‐series, elliptic curves, and odd values of the partition function
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 55-65, 1999., 1999 Let p(n) be the number of partitions of an integer n. Euler proved the following recurrence for p(n): where ω(k) = (3k 2 + k)/2. In view of Euler′s result, one sees that it is fairly easy to compute p(n) very quickly. However, many questions remain open even regarding the parity of p(n).
Nicholas Eriksson
wiley +1 more source