Results 11 to 20 of about 349 (51)
Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
Open Mathematics, 2019 Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k and only parts ±i (mod k) may be overlined ...
Liu Eric H., Du Wenjing
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Variations on a result of Bressoud [PDF]
, 2012 The well-known Rogers-Ramanujan identities have been a rich source of mathematical study over the last fifty years. In particular, Gordon’s generalization in the early 1960s led to additional work by Andrews and Bressoud in subsequent years ...
Kursungoz, Kagan +2 more
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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
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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
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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
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Some Congruences of a Restricted Bipartition Function
, 2016 Let $c_N(n)$ denotes the number of bipartitions $(\lambda, \mu)$ of a positive integer $n$ subject to the restriction that each part of $\mu$ is divisible by $N$.
Boruah, Chayanika, Saikia, Nipen
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