Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions.

Frank G. Garvan

Displaying similar documents to “Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions.”

Inductive Limits and Partitions of Unity.

Marc de Wilde (1971)

Manuscripta mathematica

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Generalizations of Schur's partition theorem.

Krishnaswami Alladi, Basil Gordon (1993)

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A combinatorial proof of Andrews' smallest parts partition function.

Ji, Kathy Qing (2008)

The Electronic Journal of Combinatorics [electronic only]

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Asymptotic formulae for partition ranks

Jehanne Dousse, Michael H. Mertens (2015)

Acta Arithmetica

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Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.

On some general problems in the theory of partitions, I

P Erdös, P. Turán (1971)

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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...