Exceptional congruences for powers of the partition function
Matthew Boylan (2004)
Acta Arithmetica
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Displaying similar documents to “An analog of crank for a certain kind of partition function arising from the cubic continued fraction”
Exceptional congruences for powers of the partition function
Partial fraction decompositions and Kummer congruences for the normalized coefficients of the Laurent expansion of elliptic functions parametrizing a nonsingular cubic curve in Hessian normal form.
Chip Snyder (1979)
Journal für die reine und angewandte Mathematik
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Self-conjugate vector partitions and the parity of the spt-function
George E. Andrews, Frank G. Garvan, Jie Liang (2013)
Acta Arithmetica
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Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first...
Congruences for Ramanujan's ϕ function
Song Heng Chan (2012)
Acta Arithmetica
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Another smallest part function related to Andrews' spt function
Alexander E. Patkowski (2015)
Acta Arithmetica
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We offer some relations and congruences for two interesting spt-type functions, which together form a relation to Andrews' spt function.
Ramanujan's cubic continued fraction revisited
Heng Huat Chan, Kok Ping Loo (2007)
Acta Arithmetica
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On normal partitions in cubic graphs
Jean-Luc Fouquet, Jean-Marie Vanherpe (2009)
Discussiones Mathematicae Graph Theory
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A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.
Quadratic congruences on average and rational points on cubic surfaces
Stephan Baier, Ulrich Derenthal (2015)
Acta Arithmetica
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We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A₅ + A₁.
Congruences in ordered pairs of partitions.
Hammond, Paul, Lewis, Richard (2004)
International Journal of Mathematics and Mathematical Sciences
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Partitions and congruences in algebras. IV. Associable systems
Tran Duc Mai (1974)
Archivum Mathematicum
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Congruences involving generalized Frobenius partitions.
Sellers, James (1993)
International Journal of Mathematics and Mathematical Sciences
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Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J
Chris Jennings-Shaffer (2016)
Acta Arithmetica
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We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. We find some of the spt-crank-type functions to have interesting representations...