Results 11 to 20 of about 50 (48)
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
q‐Analogue of a binomial coefficient congruence
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 1, Page 197-200, 1995., 1995 We establish a q‐analogue of the congruence where p is a prime and a and b are positive integers.
W. Edwin Clark
wiley +1 more source
A family of partitions with attached parts and 'N copies of N'
, 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
core +1 more source
New congruences Modulo 5 and 9 for partitions with odd parts distinct
, 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
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Congruences involving generalized Frobenius partitions
, 1992 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 413-415, 1993.
James Sellers
wiley +1 more source
Some consequences of an identity of B. Gordon
, 2004 unavailable at this time... Mathematics Subject Classification (2000): 11P83 Key words: Partitions into distinct parts, self-conjugate partitions, quintuple product identity Quaestiones Mathematicae 26(2003), 327 ...
Robbins, Neville
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