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)

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Generalizations of Schur's partition theorem.

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A combinatorial proof of Andrews' smallest parts partition function.

Ji, Kathy Qing (2008)

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Asymptotic formulae for partition ranks

Jehanne Dousse, Michael H. Mertens (2015)

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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)

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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...

Extending a recent result of Santos on partitions into odd parts.

Sellers, James A. (2003)

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Combinatorial interpretations for identities using chromatic partitions

Mateus Alegri, Wagner Ferreira Santos, Samuel Brito Silva (2021)

Czechoslovak Mathematical Journal

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We provide combinatorial interpretations for three new classes of partitions, the so-called chromatic partitions. Using only combinatorial arguments, we show that these partition identities resemble well-know ordinary partition identities.